.. -*- coding: utf-8 -*- ================================= Polyiamonds: Puzzles & Solutions ================================= :Author: David Goodger :Date: $Date: 2019-10-02 20:36:39 -0500 (Wed, 02 Oct 2019) $ :Revision: $Revision: 657 $ :Web site: http://puzzler.sourceforge.net/ :Copyright: © 1998-2015 by David J. Goodger :License: `GPL 2 <../COPYING.html>`__ .. image:: images/puzzler.png :align: center .. sidebar:: Also see: * `Hexiamond Puzzles & Solutions `_ * `Heptiamond Puzzles & Solutions `_ * `An Introduction to Polyiamonds `_ * `Notes on Polyiamonds `_ * `Polyform Puzzler: Puzzles & Solutions `_ * `Polyform Puzzler FAQ `_ (`polyform details `__, `numbers of polyforms `__, `interpreting solution files `__) .. contents:: Polyiamonds of Order 1 Through 5 ================================ These puzzles use the 1 moniamond, 1 diamond, 1 triamond, 3 tetriamonds, and 4 pentiamonds, for a total of 38 equilateral triangles. * 9x1 elongated hexagon: `23,168 solutions <../solutions/iamonds/polyiamonds-12345-elongated-hexagon-9x1.txt>`__ .. image:: images/iamonds/polyiamonds-12345-elongated-hexagon-9x1.png * 5x2 elongated hexagon ring (design by Dan Klarskov): `6,852 solutions <../solutions/iamonds/polyiamonds-12345-elongated-hexagon-5x2-ring.txt>`__ .. image:: images/iamonds/polyiamonds-12345-elongated-hexagon-5x2-ring.png * Stacked 5x1 elongated hexagons (suggested by Dan Klarskov): .. list-table:: :class: borderless * - .. figure:: images/iamonds/polyiamonds-12345-stacked-elongated-hexagons-5x1-1.png `792 solutions <../solutions/iamonds/polyiamonds-12345-stacked-elongated-hexagons-5x1-1.txt>`__ - .. figure:: images/iamonds/polyiamonds-12345-stacked-elongated-hexagons-5x1-2.png `784 solutions <../solutions/iamonds/polyiamonds-12345-stacked-elongated-hexagons-5x1-2.txt>`__ * 10x1 butterfly: `2,000 solutions <../solutions/iamonds/polyiamonds-12345-butterfly-10x1.txt>`__ .. image:: images/iamonds/polyiamonds-12345-butterfly-10x1.png * Trapezoid: `98,807 solutions <../solutions/iamonds/polyiamonds-12345-trapezoid-1.txt>`__ .. image:: images/iamonds/polyiamonds-12345-trapezoid-1.png * Irregular hexagon (design by Dan Klarskov): `611,834 solutions <../solutions/iamonds/polyiamonds-12345-irregular-hexagon-1.txt>`__ .. image:: images/iamonds/polyiamonds-12345-irregular-hexagon-1.png * Peanut (2x3 elongated hexagon with side corners omitted; design by Dan Klarskov): `240,892 solutions <../solutions/iamonds/polyiamonds-12345-peanut.txt>`__ .. image:: images/iamonds/polyiamonds-12345-peanut.png * Snowflakes: .. list-table:: :class: borderless * - .. figure:: images/iamonds/polyiamonds-12345-snowflake-1.png `6,757 solutions <../solutions/iamonds/polyiamonds-12345-snowflake-1.txt>`__ (design by Dan Klarskov) - .. figure:: images/iamonds/polyiamonds-12345-snowflake-2.png `1,240 solutions <../solutions/iamonds/polyiamonds-12345-snowflake-2.txt>`__ - .. figure:: images/iamonds/polyiamonds-12345-snowflake-3.png `466 solutions <../solutions/iamonds/polyiamonds-12345-snowflake-3.txt>`__ * Dan's menagerie (animal designs by Dan Klarskov) .. list-table:: :class: borderless * - .. figure:: images/iamonds/polyiamonds-12345-bat.png Bat: `61,251 solutions <../solutions/iamonds/polyiamonds-12345-bat.txt>`__ - .. figure:: images/iamonds/polyiamonds-12345-snake.png Snake: `2,268 solutions <../solutions/iamonds/polyiamonds-12345-snake.txt>`__ * - .. figure:: images/iamonds/polyiamonds-12345-bird-1.png Bird: `42,665 solutions <../solutions/iamonds/polyiamonds-12345-bird-1.txt>`__ - .. figure:: images/iamonds/polyiamonds-12345-crab.png Crab: `8,698 solutions <../solutions/iamonds/polyiamonds-12345-crab.txt>`__ * - .. figure:: images/iamonds/polyiamonds-12345-dog-1.png Dog: `28,614 solutions <../solutions/iamonds/polyiamonds-12345-dog-1.txt>`__ - * X (`designed for G4G10 `_): `1,182 solutions <../solutions/iamonds/polyiamonds-12345-x-1.txt>`__ .. image:: images/iamonds/polyiamonds-12345-x-1.png * Elongated hexagons on hexagons: .. list-table:: :class: borderless * - .. figure:: images/iamonds/polyiamonds-12345-elongated-hex-on-hex-1.png `2,810 solutions <../solutions/iamonds/polyiamonds-12345-elongated-hex-on-hex-1.txt>`__ (design by Dan Klarskov) - .. figure:: images/iamonds/polyiamonds-12345-elongated-hex-on-hex-2.png `310 solutions <../solutions/iamonds/polyiamonds-12345-elongated-hex-on-hex-2.txt>`__ * Hexagons with 2×1 semi-regular hexagon holes (the same as in Kadon's `Iamond Ring`_ puzzle below): .. list-table:: :class: borderless * - .. figure:: images/iamonds/polyiamonds-12345-hexagon-1.png `75,070 solutions. <../solutions/iamonds/polyiamonds-12345-hexagon-1.txt>`__ - .. figure:: images/iamonds/polyiamonds-12345-hexagon-2.png `4,594 solutions. <../solutions/iamonds/polyiamonds-12345-hexagon-2.txt>`__ One-Sided Polyiamonds of Order 1 Through 5 ========================================== These puzzles use the 1 moniamond, 1 diamond, 1 triamond, 4 one-sided tetriamonds, and 6 one-sided pentiamonds, for a total of 52 equilateral triangles. * 4x2 semi-regular hexagon: `56,524,164 solutions <../solutions/iamonds/one-sided-polyiamonds-12345-semi-regular-hexagon-4x2.txt>`__ .. image:: images/iamonds/one-sided-polyiamonds-12345-semi-regular-hexagon-4x2.png * Hexagons with two unit-triangle holes: .. list-table:: :class: borderless * - .. figure:: images/iamonds/one-sided-polyiamonds-12345-hexagon-1.png `5,085,616 solutions <../solutions/iamonds/one-sided-polyiamonds-12345-hexagon-1.txt>`__ - .. figure:: images/iamonds/one-sided-polyiamonds-12345-hexagon-2.png `6,407,224 solutions <../solutions/iamonds/one-sided-polyiamonds-12345-hexagon-2.txt>`__ * X (`designed for G4G10`_): `142,128 solutions <../solutions/iamonds/one-sided-polyiamonds-12345-x-1.txt>`__ .. image:: images/iamonds/one-sided-polyiamonds-12345-x-1.png Polyiamonds of Order 1 Through 6 ================================ These puzzles use the 1 moniamond, 1 diamond, 1 triamond, 3 tetriamonds, 4 pentiamonds, and 12 hexiamonds, for a total of 110 equilateral triangles. * 3x5 elongated hexagon: `solutions incomplete <../solutions/iamonds/polyiamonds-123456-elongated-hexagon-3x5.txt>`__ .. image:: images/iamonds/polyiamonds-123456-elongated-hexagon-3x5.png * 11x5 parallelogram: `solutions incomplete <../solutions/iamonds/polyiamonds-123456-11x5.txt>`__ .. image:: images/iamonds/polyiamonds-123456-11x5.png * 8x5 butterfly: `solutions incomplete <../solutions/iamonds/polyiamonds-123456-butterfly-8x5.txt>`__ .. image:: images/iamonds/polyiamonds-123456-butterfly-8x5.png One-Sided Polyiamonds of Order 1 Through 6 ========================================== These puzzles use the 1 moniamond, 1 diamond, 1 triamond, 4 one-sided tetriamonds, 6 one-sided pentiamonds, and 19 one-sided hexiamonds, for a total of 166 equilateral triangles. * 11x1 semi-regular hexagon: `solutions incomplete <../solutions/iamonds/one-sided-polyiamonds-123456-semi-regular-hexagon-11x1.txt>`__ .. image:: images/iamonds/one-sided-polyiamonds-123456-semi-regular-hexagon-11x1.png * Triangles: .. list-table:: :class: borderless * - .. figure:: images/iamonds/one-sided-polyiamonds-123456-triangle-1.png `solutions incomplete <../solutions/iamonds/one-sided-polyiamonds-123456-triangle-1.txt>`__ - .. figure:: images/iamonds/one-sided-polyiamonds-123456-triangle-2.png `solutions incomplete <../solutions/iamonds/one-sided-polyiamonds-123456-triangle-2.txt>`__ * - .. figure:: images/iamonds/one-sided-polyiamonds-123456-triangle-3.png `solutions incomplete <../solutions/iamonds/one-sided-polyiamonds-123456-triangle-3.txt>`__ - .. figure:: images/iamonds/one-sided-polyiamonds-123456-triangle-4.png `solutions incomplete <../solutions/iamonds/one-sided-polyiamonds-123456-triangle-4.txt>`__ * - .. figure:: images/iamonds/one-sided-polyiamonds-123456-triangle-5.png `solutions incomplete <../solutions/iamonds/one-sided-polyiamonds-123456-triangle-5.txt>`__ - .. figure:: images/iamonds/one-sided-polyiamonds-123456-triangle-6.png `solutions incomplete <../solutions/iamonds/one-sided-polyiamonds-123456-triangle-6.txt>`__ * - .. figure:: images/iamonds/one-sided-polyiamonds-123456-triangle-7.png `solutions incomplete <../solutions/iamonds/one-sided-polyiamonds-123456-triangle-7.txt>`__ - .. figure:: images/iamonds/one-sided-polyiamonds-123456-triangle-8.png `solutions incomplete <../solutions/iamonds/one-sided-polyiamonds-123456-triangle-8.txt>`__ * - .. figure:: images/iamonds/one-sided-polyiamonds-123456-triangle-9.png `solutions incomplete <../solutions/iamonds/one-sided-polyiamonds-123456-triangle-9.txt>`__ - .. figure:: images/iamonds/one-sided-polyiamonds-123456-triangle-10.png `solutions incomplete <../solutions/iamonds/one-sided-polyiamonds-123456-triangle-10.txt>`__ Polyiamonds of Order 1 Through 7 ================================ These puzzles use the 1 moniamond, 1 diamond, 1 triamond, 3 tetriamonds, 4 pentiamonds, 12 hexiamonds, and 24 heptiamonds, for a total of 278 equilateral triangles. * Hexagons: .. list-table:: :class: borderless * - .. figure:: images/iamonds/polyiamonds-1234567-hexagon-1.png `solutions incomplete <../solutions/iamonds/polyiamonds-1234567-hexagon-1.txt>`__ - .. figure:: images/iamonds/polyiamonds-1234567-hexagon-2.png `solutions incomplete <../solutions/iamonds/polyiamonds-1234567-hexagon-2.txt>`__ * - .. figure:: images/iamonds/polyiamonds-1234567-hexagon-3.png `solutions incomplete <../solutions/iamonds/polyiamonds-1234567-hexagon-3.txt>`__ - .. figure:: images/iamonds/polyiamonds-1234567-hexagon-4.png `solutions incomplete <../solutions/iamonds/polyiamonds-1234567-hexagon-4.txt>`__ * - .. figure:: images/iamonds/polyiamonds-1234567-hexagon-5.png `solutions incomplete <../solutions/iamonds/polyiamonds-1234567-hexagon-5.txt>`__ - * .. _iamond ring: `Kadon's "Iamond Ring" `_: `solutions incomplete <../solutions/iamonds/polyiamonds-1234567-iamond-ring.txt>`__ .. image:: images/iamonds/polyiamonds-1234567-iamond-ring.png The configuration above has the order 1 through 5 polyiamonds (moniamond, diamond, triamond, tetriamonds, & pentiamonds) restricted to an inner ring; the hexiamonds restricted to an intermediate ring; and the heptiamonds restricted to an outer ring. The coloured version below shows the moniamond in black, the diamond in gray, the triamond in purple, the tetriamonds in blue, the pentiamonds in green, the hexiamonds in red, and the heptiamonds in orange. .. image:: images/iamonds/polyiamonds-1234567-iamond-ring-coloured.png * 2x10 elongated hexagon: `solutions incomplete <../solutions/iamonds/polyiamonds-1234567-elongated-hexagon-2x10-1.txt>`__ .. image:: images/iamonds/polyiamonds-1234567-elongated-hexagon-2x10-1.png * 12x10 butterfly: `solutions incomplete <../solutions/iamonds/polyiamonds-1234567-butterfly-12x10-1.txt>`__ .. image:: images/iamonds/polyiamonds-1234567-butterfly-12x10-1.png