.. -*- coding: utf-8 -*- ============================================================ Polytwigs (Hexagonal-Grid Polysticks): Puzzles & Solutions ============================================================ :Author: David Goodger :Date: $Date: 2015-02-24 14:21:02 -0600 (Tue, 24 Feb 2015) $ :Revision: $Revision: 600 $ :Web site: http://puzzler.sourceforge.net/ :Copyright: |c| 1998-2015 by David J. Goodger :License: `GPL 2 <../COPYING.html>`__ .. image:: images/puzzler.png :align: center .. sidebar:: Also see: * `An Introduction to Polytwigs `_ * `Notes on Polytwigs `_ * `Polysticks: Puzzles & Solutions `_ * `Polytrigs (Triangular-Grid Polysticks): Puzzles & Solutions `_ * `An Introduction to Polytrigs (Triangular-Grid Polysticks) `_ * `Polyform Puzzler: Puzzles & Solutions `_ * `Polyform Puzzler FAQ `_ (`polyform details `__, `numbers of polyforms `__, `interpreting solution files `__) .. contents:: One-Sided Polytwigs of Order 1 Through 3 ======================================== This puzzle uses the 1 monotwig, 1 ditwig, and 4 one-sided tritwigs,, for a total of 15 line segments on the hexagonal grid. * Triangle: `3 solutions <../solutions/twigs/one-sided-polytwigs-123-triangle.txt>`__ .. image:: images/twigs/one-sided-polytwigs-123-triangle.png Tetratwigs ========== This puzzle uses the 4 tetratwigs for a total of 16 line segments on the hexagonal grid. * Arch: `2 solutions <../solutions/twigs/tetratwigs-arch.txt>`__ .. image:: images/twigs/tetratwigs-arch.png One-Sided Tetratwigs ==================== These puzzles use the 6 one-sided tetratwigs for a total of 24 line segments on the hexagonal grid. * Triangles with 3 line segments omitted in various positions: .. list-table:: :class: borderless * - .. figure:: images/twigs/one-sided-tetratwigs-triangle-1.png `2 solutions <../solutions/twigs/one-sided-tetratwigs-triangle-1.txt>`__ - .. figure:: images/twigs/one-sided-tetratwigs-triangle-2.png `1 solution <../solutions/twigs/one-sided-tetratwigs-triangle-2.txt>`__ - .. figure:: images/twigs/one-sided-tetratwigs-triangle-3.png `2 solutions <../solutions/twigs/one-sided-tetratwigs-triangle-3.txt>`__ - .. figure:: images/twigs/one-sided-tetratwigs-triangle-4.png `1 solution <../solutions/twigs/one-sided-tetratwigs-triangle-4.txt>`__ * Arches with 2 line segments omitted in various positions: .. list-table:: :class: borderless * - .. figure:: images/twigs/one-sided-tetratwigs-arch-1.png `1 solution <../solutions/twigs/one-sided-tetratwigs-arch-1.txt>`__ - .. figure:: images/twigs/one-sided-tetratwigs-arch-2.png `1 solution <../solutions/twigs/one-sided-tetratwigs-arch-2.txt>`__ - .. figure:: images/twigs/one-sided-tetratwigs-arch-3.png `1 solution <../solutions/twigs/one-sided-tetratwigs-arch-3.txt>`__ - .. figure:: images/twigs/one-sided-tetratwigs-arch-4.png `1 solution <../solutions/twigs/one-sided-tetratwigs-arch-4.txt>`__ Polytwigs of Order 1 Through 4 ============================== These puzzles use the 1 monotwig, 1 ditwig, 3 tritwigs, and 4 tetratwigs, for a total of 28 line segments on the hexagonal grid. * Hexagons with 2 line segments omitted in various positions: .. list-table:: :class: borderless * - .. figure:: images/twigs/polytwigs-1234-hex-1.png `1175 solutions <../solutions/twigs/polytwigs-1234-hex-1.txt>`__ - .. figure:: images/twigs/polytwigs-1234-hex-2.png `1506 solutions <../solutions/twigs/polytwigs-1234-hex-2.txt>`__ - .. figure:: images/twigs/polytwigs-1234-hex-3.png `2019 solutions <../solutions/twigs/polytwigs-1234-hex-3.txt>`__ * - .. figure:: images/twigs/polytwigs-1234-hex-4.png `2007 solutions <../solutions/twigs/polytwigs-1234-hex-4.txt>`__ - .. figure:: images/twigs/polytwigs-1234-hex-5.png `958 solutions <../solutions/twigs/polytwigs-1234-hex-5.txt>`__ - .. figure:: images/twigs/polytwigs-1234-hex-6.png `962 solutions <../solutions/twigs/polytwigs-1234-hex-6.txt>`__ * 4x2 inset rectangle: `5,755 solutions <../solutions/twigs/polytwigs-1234-inset-rectangle-4x2.txt>`__ .. image:: images/twigs/polytwigs-1234-inset-rectangle-4x2.png One-Sided Polytwigs of Order 1 Through 4 ======================================== These puzzles use the 1 monotwig, 1 ditwig, 4 one-sided tritwigs, and 6 one-sided tetratwigs, for a total of 39 line segments on the hexagonal grid. * 5x2 trapezoid: `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-trapezoid-5x2.txt>`__ .. image:: images/twigs/one-sided-polytwigs-1234-trapezoid-5x2.png * 3x2 elongated hexagons with 2 segments omitted in various positions: .. list-table:: :class: borderless * - .. figure:: images/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-1.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-1.txt>`__ - .. figure:: images/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-2.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-2.txt>`__ - .. figure:: images/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-3.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-3.txt>`__ - .. figure:: images/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-4.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-4.txt>`__ * - .. figure:: images/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-5.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-5.txt>`__ - .. figure:: images/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-6.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-6.txt>`__ - .. figure:: images/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-7.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-7.txt>`__ - .. figure:: images/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-8.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-elongated-hexagon-3x2-8.txt>`__ * Triangles: .. list-table:: :class: borderless * - .. figure:: images/twigs/one-sided-polytwigs-1234-triangle-1.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-triangle-1.txt>`__ - .. figure:: images/twigs/one-sided-polytwigs-1234-triangle-2.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-triangle-2.txt>`__ - .. figure:: images/twigs/one-sided-polytwigs-1234-triangle-3.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-triangle-3.txt>`__ - .. figure:: images/twigs/one-sided-polytwigs-1234-triangle-4.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-1234-triangle-4.txt>`__ Pentatwigs ========== These puzzles use the 12 pentatwigs (a.k.a. pentacules), for a total of 60 line segments on the hexagonal grid. * Triangle: `56 solutions <../solutions/twigs/pentatwigs-triangle.txt>`__ .. image:: images/twigs/pentatwigs-triangle.png * Triangle variations (puzzle designs by Colin F. Brown): .. list-table:: :class: borderless * - .. figure:: images/twigs/pentatwigs-triangle-2.png `6 solutions <../solutions/twigs/pentatwigs-triangle-2.txt>`__ - .. figure:: images/twigs/pentatwigs-triangle-3.png `2 solutions <../solutions/twigs/pentatwigs-triangle-3.txt>`__ * 5x3 parallelogram: `194 solutions <../solutions/twigs/pentatwigs-5x3.txt>`__ .. image:: images/twigs/pentatwigs-5x3.png * 4x4 parallelograms: .. list-table:: :class: borderless * - .. figure:: images/twigs/pentatwigs-4x4-1.png `1 solution <../solutions/twigs/pentatwigs-4x4-1.txt>`__ (design by Colin F. Brown) - .. figure:: images/twigs/pentatwigs-4x4-2.png `8 solutions <../solutions/twigs/pentatwigs-4x4-2.txt>`__ * 6x3 trapezoid: `184 solutions <../solutions/twigs/pentatwigs-trapezoid-6x3.txt>`__ .. image:: images/twigs/pentatwigs-trapezoid-6x3.png * 5x3 staggered rectangle: `145 solutions <../solutions/twigs/pentatwigs-staggered-rectangle-5x3.txt>`__ .. image:: images/twigs/pentatwigs-staggered-rectangle-5x3.png * 5x3 wave-staggered rectangle (puzzle design by Colin F. Brown): `202 solutions <../solutions/twigs/pentatwigs-wave-staggered-rectangle-5x3.txt>`__ .. image:: images/twigs/pentatwigs-wave-staggered-rectangle-5x3.png * 3x3 chevron: `115 solutions <../solutions/twigs/pentatwigs-chevron-3x3.txt>`__ .. image:: images/twigs/pentatwigs-chevron-3x3.png * 5x2 chevron: `241 solutions <../solutions/twigs/pentatwigs-chevron-5x2.txt>`__ .. image:: images/twigs/pentatwigs-chevron-5x2.png * Butterfly: `8 solutions <../solutions/twigs/pentatwigs-butterfly-1.txt>`__ .. image:: images/twigs/pentatwigs-butterfly-1.png * Trefoil (puzzle design by Colin F. Brown): `4 solutions <../solutions/twigs/pentatwigs-trefoil.txt>`__ .. image:: images/twigs/pentatwigs-trefoil.png If you look carefully, you can see that the solution above consists of 3 congruent shapes (in fact, all 4 solutions share this property). This is illustrated explicitly in the following exploded form (same `4 solutions <../solutions/twigs/pentatwigs-3-congruent-1.txt>`__, just rearranged): .. image:: images/twigs/pentatwigs-3-congruent-1.png * Möbius strip (puzzle design by Colin F. Brown): `6 solutions? <../solutions/twigs/pentatwigs-mobius-strip-1.txt>`__ .. image:: images/twigs/pentatwigs-mobius-strip-1.png Take the puzzle strip above, give one end a half-twist, and join it to the other end, resulting in a `Möbius strip`__, a surface with only one side and one edge. __ http://en.wikipedia.org/wiki/M%C3%B6bius_strip This puzzle was implemented without any coordinate "wrap-around": a piece cannot begin at the right edge and continue (through the join) to the left edge. There may be many more solutions with such a wrap-around configuration. * Elongated rounded rectangle (design by Colin F. Brown): `21 solutions <../solutions/twigs/pentatwigs-elongated-rounded-rectangle-1.txt>`__ .. image:: images/twigs/pentatwigs-elongated-rounded-rectangle-1.png * Rosette clusters (design by Colin F. Brown): .. list-table:: :class: borderless * - .. figure:: images/twigs/pentatwigs-rosette-cluster-1.png `9 solutions <../solutions/twigs/pentatwigs-rosette-cluster-1.txt>`__ - .. figure:: images/twigs/pentatwigs-rosette-cluster-2.png `11 solutions <../solutions/twigs/pentatwigs-rosette-cluster-2.txt>`__ * X (`designed for G4G10 `_): `32 solutions <../solutions/twigs/pentatwigs-x-1.txt>`__ .. image:: images/twigs/pentatwigs-x-1.png * 5x2 elongated hexagon (with holes; puzzle design by Colin F. Brown): `2 solutions <../solutions/twigs/pentatwigs-elongated-hexagon-5x2-1.txt>`__ .. image:: images/twigs/pentatwigs-elongated-hexagon-5x2-1.png One-Sided Pentatwigs ==================== These puzzles use the 19 one-sided pentatwigs, for a total of 95 line segments on the hexagonal grid. * 12x2 trapezoid: `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-trapezoid-12x2.txt>`__ .. image:: images/twigs/one-sided-pentatwigs-trapezoid-12x2.png * 7x4 inset rectangle with 1 segment omitted in various positions: .. list-table:: :class: borderless * - .. figure:: images/twigs/one-sided-pentatwigs-inset-rectangle-7x4-1.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-inset-rectangle-7x4-1.txt>`__ - .. figure:: images/twigs/one-sided-pentatwigs-inset-rectangle-7x4-2.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-inset-rectangle-7x4-2.txt>`__ * - .. figure:: images/twigs/one-sided-pentatwigs-inset-rectangle-7x4-3.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-inset-rectangle-7x4-3.txt>`__ - .. figure:: images/twigs/one-sided-pentatwigs-inset-rectangle-7x4-4.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-inset-rectangle-7x4-4.txt>`__ * 8x2 elongated hexagons (with holes): .. list-table:: :class: borderless * - .. figure:: images/twigs/one-sided-pentatwigs-elongated-hexagon-8x2-1.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-elongated-hexagon-8x2-1.txt>`__ - .. figure:: images/twigs/one-sided-pentatwigs-elongated-hexagon-8x2-2.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-elongated-hexagon-8x2-2.txt>`__ * 3x4 elongated hexagons (with holes): .. list-table:: :class: borderless * - .. figure:: images/twigs/one-sided-pentatwigs-elongated-hexagon-3x4-1.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-elongated-hexagon-3x4-1.txt>`__ - .. figure:: images/twigs/one-sided-pentatwigs-elongated-hexagon-3x4-2.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-elongated-hexagon-3x4-2.txt>`__ * String of rosettes (design by `Peter F. Esser`_): `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-rosettes-1.txt>`__ .. image:: images/twigs/one-sided-pentatwigs-rosettes-1.png * Cross (design by `Peter F. Esser`_): `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-cross-1.txt>`__ .. image:: images/twigs/one-sided-pentatwigs-cross-1.png * Peanuts: .. list-table:: :class: borderless * - .. figure:: images/twigs/one-sided-pentatwigs-peanut-1.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-peanut-1.txt>`__ (design by `Peter F. Esser`_) - .. figure:: images/twigs/one-sided-pentatwigs-peanut-2.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-peanut-2.txt>`__ * - .. figure:: images/twigs/one-sided-pentatwigs-peanut-3.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-peanut-3.txt>`__ - .. figure:: images/twigs/one-sided-pentatwigs-peanut-4.png `solutions incomplete <../solutions/twigs/one-sided-pentatwigs-peanut-4.txt>`__ Polytwigs of Order 4 & 5 ======================== These puzzles use the 4 tetratwigs and 12 pentatwigs, for a total of 76 line segments on the hexagonal grid. * Triangle: `solutions incomplete <../solutions/twigs/polytwigs-45-triangle-1.txt>`__ .. image:: images/twigs/polytwigs-45-triangle-1.png * Diamond ring: `solutions incomplete <../solutions/twigs/polytwigs-45-diamond-ring.txt>`__ .. image:: images/twigs/polytwigs-45-diamond-ring.png * 4x3 elongated hexagon ring: `solutions incomplete <../solutions/twigs/polytwigs-45-elongated-hexagon-4x3-ring.txt>`__ .. image:: images/twigs/polytwigs-45-elongated-hexagon-4x3-ring.png * 5x3 butterfly ring: `solutions incomplete <../solutions/twigs/polytwigs-45-butterfly-5x3-ring.txt>`__ .. image:: images/twigs/polytwigs-45-butterfly-5x3-ring.png * 5x5 inset rectangle ring: `solutions incomplete <../solutions/twigs/polytwigs-45-inset-rectangle-5x5-ring.txt>`__ .. image:: images/twigs/polytwigs-45-inset-rectangle-5x5-ring.png * _`Four congruent groups`: Colin F. Brown posed this problem: divide the twelve pentatwigs into four groups of three, add one of the tetratwigs to each group. Now find a 19-line region that each (equally divided) group will tile. Mr. Brown provided one solution: .. figure:: images/twigs/polytwigs-45-four-congruent-1.png Example 1 of four congruent groups from the tetratwigs & pentatwigs: `19 solutions <../solutions/twigs/polytwigs-45-four-congruent-1.txt>`__. Others are possible: .. figure:: images/twigs/polytwigs-45-four-congruent-2.png Example 2 of four congruent groups from the tetratwigs & pentatwigs: `38 solutions <../solutions/twigs/polytwigs-45-four-congruent-2.txt>`__. **Open Problem: Combined Symmetrical Shape** Find a solution to the four congruent groups problem such that the four groups can be combined into a symmetrical shape. The more symmetries the better. The best case I have been able to come up with so far: .. figure:: images/twigs/polytwigs-45-four-congruent-3.png Example 3 of four congruent groups from the tetratwigs & pentatwigs: `2 solutions <../solutions/twigs/polytwigs-45-four-congruent-3.txt>`__. .. figure:: images/twigs/polytwigs-45-four-congruent-3-combined.png Example 3, combined: one symmetry (180° rotational); `24 solutions when restricted to combinations of the congruent shapes above <../solutions/twigs/polytwigs-45-four-congruent-3-combined.txt>`__; many solutions if unrestricted. Polytwigs of Order 1 Through 5 ============================== These puzzles use the 1 monotwig, 1 ditwig, 3 tritwigs, 4 tetratwigs, and 12 pentatwigs, for a total of 88 line segments on the hexagonal grid. * 5x5 inset rectangle: `solutions incomplete <../solutions/twigs/polytwigs-12345-inset-rectangle-5x5.txt>`__ .. image:: images/twigs/polytwigs-12345-inset-rectangle-5x5.png * 6x4 parallelograms with 3 segments omitted in various positions: .. list-table:: :class: borderless * - .. figure:: images/twigs/polytwigs-12345-6x4-1.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-1.txt>`__ - .. figure:: images/twigs/polytwigs-12345-6x4-2.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-2.txt>`__ * - .. figure:: images/twigs/polytwigs-12345-6x4-3.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-3.txt>`__ - .. figure:: images/twigs/polytwigs-12345-6x4-4.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-4.txt>`__ * - .. figure:: images/twigs/polytwigs-12345-6x4-5.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-5.txt>`__ - .. figure:: images/twigs/polytwigs-12345-6x4-6.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-6.txt>`__ * - .. figure:: images/twigs/polytwigs-12345-6x4-7.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-7.txt>`__ - .. figure:: images/twigs/polytwigs-12345-6x4-8.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-8.txt>`__ * - .. figure:: images/twigs/polytwigs-12345-6x4-9.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-9.txt>`__ - .. figure:: images/twigs/polytwigs-12345-6x4-10.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-10.txt>`__ * - .. figure:: images/twigs/polytwigs-12345-6x4-11.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-11.txt>`__ - .. figure:: images/twigs/polytwigs-12345-6x4-12.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-12.txt>`__ * - .. figure:: images/twigs/polytwigs-12345-6x4-13.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-13.txt>`__ - .. figure:: images/twigs/polytwigs-12345-6x4-14.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-14.txt>`__ * - .. figure:: images/twigs/polytwigs-12345-6x4-15.png `solutions incomplete <../solutions/twigs/polytwigs-12345-6x4-15.txt>`__ - * 9x3 trapezoid ring: `solutions incomplete <../solutions/twigs/polytwigs-12345-trapezoid-ring-9x3.txt>`__ .. image:: images/twigs/polytwigs-12345-trapezoid-ring-9x3.png * 4x3 elongated hexagon with 1 segment omitted: `solutions incomplete <../solutions/twigs/polytwigs-12345-elongated-hexagon-4x3.txt>`__ .. image:: images/twigs/polytwigs-12345-elongated-hexagon-4x3.png * 8x2 butterfly with 2 segments omitted in various positions: .. list-table:: :class: borderless * - .. figure:: images/twigs/polytwigs-12345-butterfly-8x2-1.png `solutions incomplete <../solutions/twigs/polytwigs-12345-butterfly-8x2-1.txt>`__ - .. figure:: images/twigs/polytwigs-12345-butterfly-8x2-2.png `solutions incomplete <../solutions/twigs/polytwigs-12345-butterfly-8x2-2.txt>`__ * - .. figure:: images/twigs/polytwigs-12345-butterfly-8x2-3.png `solutions incomplete <../solutions/twigs/polytwigs-12345-butterfly-8x2-3.txt>`__ - .. figure:: images/twigs/polytwigs-12345-butterfly-8x2-4.png `solutions incomplete <../solutions/twigs/polytwigs-12345-butterfly-8x2-4.txt>`__ One-Sided Polytwigs of Order 1 Through 5 ======================================== These puzzles use the 1 monotwig, 1 ditwig, 4 one-sided tritwigs, 6 one-sided tetratwigs, and 19 one-sided pentatwigs, for a total of 134 line segments on the hexagonal grid. * 12x2 butterfly: `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-butterfly-12x2.txt>`__ .. image:: images/twigs/one-sided-polytwigs-12345-butterfly-12x2.png * 12x3 parallelogram with 3 segments omitted in various positions: .. list-table:: :class: borderless * - .. figure:: images/twigs/one-sided-polytwigs-12345-12x3-1.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-12x3-1.txt>`__ * - .. figure:: images/twigs/one-sided-polytwigs-12345-12x3-2.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-12x3-2.txt>`__ * - .. figure:: images/twigs/one-sided-polytwigs-12345-12x3-3.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-12x3-3.txt>`__ * - .. figure:: images/twigs/one-sided-polytwigs-12345-12x3-4.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-12x3-4.txt>`__ * - .. figure:: images/twigs/one-sided-polytwigs-12345-12x3-5.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-12x3-5.txt>`__ * - .. figure:: images/twigs/one-sided-polytwigs-12345-12x3-6.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-12x3-6.txt>`__ * 13x3 trapezoid with 3 segments omitted in various positions: .. list-table:: :class: borderless * - .. figure:: images/twigs/one-sided-polytwigs-12345-trapezoid-13x3-1.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-trapezoid-13x3-1.txt>`__ * - .. figure:: images/twigs/one-sided-polytwigs-12345-trapezoid-13x3-2.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-trapezoid-13x3-2.txt>`__ * - .. figure:: images/twigs/one-sided-polytwigs-12345-trapezoid-13x3-3.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-trapezoid-13x3-3.txt>`__ * - .. figure:: images/twigs/one-sided-polytwigs-12345-trapezoid-13x3-4.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-trapezoid-13x3-4.txt>`__ * - .. figure:: images/twigs/one-sided-polytwigs-12345-trapezoid-13x3-5.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-trapezoid-13x3-5.txt>`__ * - .. figure:: images/twigs/one-sided-polytwigs-12345-trapezoid-13x3-6.png `solutions incomplete <../solutions/twigs/one-sided-polytwigs-12345-trapezoid-13x3-6.txt>`__ Hexatwigs ========= These puzzles use the 27 hexatwigs, for a total of 162 line segments on the hexagonal grid. * Triangle: `solutions incomplete <../solutions/twigs/hexatwigs-triangle.txt>`__ .. image:: images/twigs/hexatwigs-triangle.png * Triangle rings: .. list-table:: :class: borderless * - .. figure:: images/twigs/hexatwigs-triangle-ring-1.png `solutions incomplete <../solutions/twigs/hexatwigs-triangle-ring-1.txt>`__ (design by `Peter F. Esser`_) - .. figure:: images/twigs/hexatwigs-triangle-ring-2.png `solutions incomplete <../solutions/twigs/hexatwigs-triangle-ring-2.txt>`__ (design by `Peter F. Esser`_) * 14x2 elongated hexagon: `solutions incomplete <../solutions/twigs/hexatwigs-elongated-hexagon-14x2.txt>`__ .. image:: images/twigs/hexatwigs-elongated-hexagon-14x2.png * Hexagon rings: .. list-table:: :class: borderless * - .. figure:: images/twigs/hexatwigs-hexagon-ring-1.png `solutions incomplete <../solutions/twigs/hexatwigs-hexagon-ring-1.txt>`__ (design by `Peter F. Esser`_) - .. figure:: images/twigs/hexatwigs-hexagon-ring-2.png `solutions incomplete <../solutions/twigs/hexatwigs-hexagon-ring-2.txt>`__ * - .. figure:: images/twigs/hexatwigs-hexagon-ring-3.png `solutions incomplete <../solutions/twigs/hexatwigs-hexagon-ring-3.txt>`__ - .. figure:: images/twigs/hexatwigs-hexagon-ring-4.png `solutions incomplete <../solutions/twigs/hexatwigs-hexagon-ring-4.txt>`__ * Elongated hexagon ring (design by `Peter F. Esser`_): `solutions incomplete <../solutions/twigs/hexatwigs-elongated-hexagon-ring.txt>`__ .. image:: images/twigs/hexatwigs-elongated-hexagon-ring.png * 6x3 semiregular hexagon: `solutions incomplete <../solutions/twigs/hexatwigs-semiregular-hexagon-6x3.txt>`__ .. image:: images/twigs/hexatwigs-semiregular-hexagon-6x3.png This solution was first found by `Peter F. Esser`_. * Knobbed hexagon: `solutions incomplete <../solutions/twigs/hexatwigs-knobbed-hexagon.txt>`__ .. image:: images/twigs/hexatwigs-knobbed-hexagon.png * X (`designed for G4G10`_): .. list-table:: :class: borderless * - .. figure:: images/twigs/hexatwigs-x-1.png `1: solutions incomplete <../solutions/twigs/hexatwigs-x-1.txt>`__ - .. figure:: images/twigs/hexatwigs-x-2.png `2: solutions incomplete <../solutions/twigs/hexatwigs-x-2.txt>`__ * - .. figure:: images/twigs/hexatwigs-x-3.png `3: solutions incomplete <../solutions/twigs/hexatwigs-x-3.txt>`__ - .. figure:: images/twigs/hexatwigs-x-4.png `4: solutions incomplete <../solutions/twigs/hexatwigs-x-4.txt>`__ * - .. figure:: images/twigs/hexatwigs-x-5.png `5: solutions incomplete <../solutions/twigs/hexatwigs-x-5.txt>`__ - .. figure:: images/twigs/hexatwigs-x-6.png `6: solutions incomplete <../solutions/twigs/hexatwigs-x-6.txt>`__ * Trefoils: .. list-table:: :class: borderless * - .. figure:: images/twigs/hexatwigs-trefoil-1.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-1.txt>`__ (design by `Peter F. Esser`_) - .. figure:: images/twigs/hexatwigs-trefoil-2.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-2.txt>`__ (design by `Peter F. Esser`_) * - .. figure:: images/twigs/hexatwigs-trefoil-3.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-3.txt>`__ (design by `Peter F. Esser`_) - .. figure:: images/twigs/hexatwigs-trefoil-3-esser-small.jpg :target: images/twigs/hexatwigs-trefoil-3-esser.jpg "Hexatwigs trefoil 3" built from pieces laser-cut from 5mm acrylic (`using this file`__). Puzzle pieces, solution, and photograph by `Peter F. Esser`_. Click for the full-size image. __ images/twigs/hexatwigs-pieces-esser.svg * - .. figure:: images/twigs/hexatwigs-trefoil-4.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-4.txt>`__ - .. figure:: images/twigs/hexatwigs-trefoil-5.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-5.txt>`__ * - .. figure:: images/twigs/hexatwigs-trefoil-6.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-6.txt>`__ - .. figure:: images/twigs/hexatwigs-trefoil-7.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-7.txt>`__ * - .. figure:: images/twigs/hexatwigs-trefoil-8.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-8.txt>`__ - .. figure:: images/twigs/hexatwigs-trefoil-9.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-9.txt>`__ * - .. figure:: images/twigs/hexatwigs-trefoil-10.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-10.txt>`__ - .. figure:: images/twigs/hexatwigs-trefoil-11.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-11.txt>`__ * - .. figure:: images/twigs/hexatwigs-trefoil-12.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-12.txt>`__ - .. figure:: images/twigs/hexatwigs-trefoil-13.png `solutions incomplete <../solutions/twigs/hexatwigs-trefoil-13.txt>`__ One-Sided Hexatwigs =================== These puzzles use the 49 one-sided hexatwigs, for a total of 294 line segments on the hexagonal grid. * Hexagon ring: `solutions incomplete <../solutions/twigs/one-sided-hexatwigs-hexagon-ring.txt>`__ .. image:: images/twigs/one-sided-hexatwigs-hexagon-ring.png This solution was first found by `Peter F. Esser`_. * 26x2 elongated hexagon (design by `Peter F. Esser`_): `solutions incomplete <../solutions/twigs/one-sided-hexatwigs-elongated-hexagon-26x2.txt>`__ .. image:: images/twigs/one-sided-hexatwigs-elongated-hexagon-26x2.png Polytwigs of Order 1 Through 6 ============================== These puzzles use the 1 monotwig, 1 ditwig, 3 tritwigs, 4 tetratwigs, 12 pentatwigs, and 27 hexatwigs, for a total of 250 line segments on the hexagonal grid. * 22x2 elongated hexagon (design by `Peter F. Esser`_): `solutions incomplete <../solutions/twigs/polytwigs-123456-elongated-hexagon-22x2.txt>`__ .. image:: images/twigs/polytwigs-123456-elongated-hexagon-22x2.png Quasi-Tritwigs ============== These puzzles use the 17 quasi-tritwigs, for a total of 51 line segments on the hexagonal grid. See `Quasi-Polyforms`_ in `An Introduction to Polytwigs`_. .. _Quasi-Polyforms: polytwigs-intro.html#quasi-polyforms * 10x1 parallelogram (design by Colin F. Brown): `solutions incomplete <../solutions/twigs/quasi-tritwigs-10x1.txt>`__ .. image:: images/twigs/quasi-tritwigs-10x1.png * 6x2 parallelogram: `solutions incomplete <../solutions/twigs/quasi-tritwigs-6x2.txt>`__ .. image:: images/twigs/quasi-tritwigs-6x2.png * Triangles: .. list-table:: :class: borderless * - .. figure:: images/twigs/quasi-tritwigs-triangle-1.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-triangle-1.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-triangle-2.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-triangle-2.txt>`__ * - .. figure:: images/twigs/quasi-tritwigs-triangle-3.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-triangle-3.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-triangle-4.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-triangle-4.txt>`__ * Snowflakes: .. list-table:: :class: borderless * - .. figure:: images/twigs/quasi-tritwigs-snowflake-1.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-snowflake-1.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-snowflake-2.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-snowflake-2.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-snowflake-3.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-snowflake-3.txt>`__ * 2x3 elongated hexagons: .. list-table:: :class: borderless * - .. figure:: images/twigs/quasi-tritwigs-elongated-hexagon-2x3-1.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-elongated-hexagon-2x3-1.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-elongated-hexagon-2x3-2.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-elongated-hexagon-2x3-2.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-elongated-hexagon-2x3-3.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-elongated-hexagon-2x3-3.txt>`__ * - .. figure:: images/twigs/quasi-tritwigs-elongated-hexagon-2x3-4.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-elongated-hexagon-2x3-4.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-elongated-hexagon-2x3-5.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-elongated-hexagon-2x3-5.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-elongated-hexagon-2x3-6.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-elongated-hexagon-2x3-6.txt>`__ * Trefoils: .. list-table:: :class: borderless * - .. figure:: images/twigs/quasi-tritwigs-trefoil-1.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-trefoil-1.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-trefoil-2.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-trefoil-2.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-trefoil-3.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-trefoil-3.txt>`__ * - .. figure:: images/twigs/quasi-tritwigs-trefoil-4.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-trefoil-4.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-trefoil-5.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-trefoil-5.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-trefoil-6.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-trefoil-6.txt>`__ * - .. figure:: images/twigs/quasi-tritwigs-trefoil-7.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-trefoil-7.txt>`__ - .. figure:: images/twigs/quasi-tritwigs-trefoil-8.png `solutions incomplete <../solutions/twigs/quasi-tritwigs-trefoil-8.txt>`__ - Quasi-Polytwigs of Order 1 Through 3 ==================================== These puzzles use the monotwig, the 3 quasi-ditwigs, 17 quasi-tritwigs, for a total of 58 line segments on the hexagonal grid. See `Quasi-Polyforms`_ in `An Introduction to Polytwigs`_. * 9x2 rounded rectangle: `solutions incomplete <../solutions/twigs/quasi-polytwigs-123-rounded-rectangle-9x2.txt>`__ .. image:: images/twigs/quasi-polytwigs-123-rounded-rectangle-9x2.png * Hexagon rings: .. list-table:: :class: borderless * - .. figure:: images/twigs/quasi-polytwigs-123-hexagon-ring-1.png `solutions incomplete <../solutions/twigs/quasi-polytwigs-123-hexagon-ring-1.txt>`__ - .. figure:: images/twigs/quasi-polytwigs-123-hexagon-ring-2.png `solutions incomplete <../solutions/twigs/quasi-polytwigs-123-hexagon-ring-2.txt>`__ * - .. figure:: images/twigs/quasi-polytwigs-123-hexagon-ring-3.png `solutions incomplete <../solutions/twigs/quasi-polytwigs-123-hexagon-ring-3.txt>`__ - .. figure:: images/twigs/quasi-polytwigs-123-hexagon-ring-4.png `solutions incomplete <../solutions/twigs/quasi-polytwigs-123-hexagon-ring-4.txt>`__ * 5x3 parallelogram ring: `solutions incomplete <../solutions/twigs/quasi-polytwigs-123-5x3-parallelogram-ring.txt>`__ .. image:: images/twigs/quasi-polytwigs-123-5x3-parallelogram-ring.png * 6x3 trapezoid ring: `solutions incomplete <../solutions/twigs/quasi-polytwigs-123-6x3-trapezoid-ring.txt>`__ .. image:: images/twigs/quasi-polytwigs-123-6x3-trapezoid-ring.png .. _Peter F. Esser: http://polyforms.eu/ .. |c| unicode:: U+00A9 .. copyright sign