Polyhexes: Puzzles & Solutions
| Author: | David Goodger <goodger@python.org> |
|---|---|
| Date: | 2015-02-24 |
| Revision: | 600 |
| Web site: | http://puzzler.sourceforge.net/ |
| Copyright: | © 1998-2015 by David J. Goodger |
| License: | GPL 2 |
Contents
Tetrahexes
The 7 tetrahexes total 28 hexagons. Unfortunately, there is no solution to the order-7 triangle using all seven tetrahexes (a tiling using seven copies of the P4 tetrahex is possible).
4x7 parallelogram: 9 solutions
9x2 elongated hexagon (= 3x10 parallelogram with corners clipped, the old name): 2 solutions
3x4 elongated hexagons with holes:
2 solutions (design by Abaroth)
3 solutions (design by Abaroth)
4 solutions (design by Abaroth)
5 solutions (design by Abaroth)
5x7 "coin" (5x3 elongated hexagon with central hole): 4 solutions
Two intersecting diamonds:
Flowers:
4 solutions (design by George Sicherman)
1 solution (design by Abaroth)
Bumpy triangle: 1 solution
7x4 staggered rectangle: 23 solutions
Holey Star (design by George Sicherman): 2 solutions
Trihexes & Tetrahexes: Polyhexes of Order 3 & 4
These puzzles use the three trihexes and the seven tetrahexes, for a total of 37 hexagons. This combination was featured in The Puzzling World of Polyhedral Dissections, by Stewart T. Coffin and produced as the Snowflake puzzle.
Hexagon: 12,290 solutions
Hexagram: 167 solutions
Tri-lobed Crowns:
Polyhexes of Order 1 Through 4
These puzzles use the monohex, the dihex, the three trihexes, and the seven tetrahexes, for a total of 40 hexagons.
4x10 parallelogram: 3,665,348 solutions
5x8 parallelogram: 7,578,295 solutions
6x7 parallelogram with hole (design by Dan Klarskov): 3,832,702 solutions
13x2 elongated hexagon: 1,389,980 solutions
3x5 elongated hexagon (design by Dan Klarskov): 6,175,571 solutions
Irregular hexagons:
37,293,445 solutions (design by Dan Klarskov)
655,208 solutions (design by Dan Klarskov)
1,361,945 solutions (design by Dan Klarskov)
50,041,967 solutions (design by Kate Jones)
9x8 trapezoid (design by Dan Klarskov): 1,310,969 solutions
Triangles:
Tri-lobed Crown (inspired by the Snowflake puzzle): 1,349,201 solutions
Jagged hexagons:
213,477 solutions (design by Dan Klarskov)
70,634 solutions (design by Kate Jones)
247,392 solutions (design by Kate Jones)
Knobbed hexagons:
17,683 solutions (design by Dan Klarskov)
2x6 elongated hexagon ring (design by Dan Klarskov): 659,517 solutions
Diamond ring (design by Dan Klarskov): 83,837 solutions
Hexagon rings:
Equivalent to the inner ring of the featured solution of Kadon's "Hexnut" puzzle; see the full Hexnut puzzle.Staggered rectangles:
solutions incomplete (design by Dan Klarskov)
One-Sided Polyhexes of Order 1 Through 4
These puzzles use the monohex, the dihex, the three trihexes, and the ten one-sided tetrahexes, for a total of 52 hexagons.
Polyhexes of Order 1 Through 5
These puzzles uses the monohex, the dihex, the three trihexes, the seven tetrahexes, and the 22 pentahexes, for a total of 150 hexagons.
5x30 parallelogram: solutions incomplete
6x25 parallelogram: solutions incomplete
10x15 parallelogram: solutions incomplete
Hexagon ring (equivalent to Kadon's "Hexnut" puzzle, and subdivided similarly to the featured solution by Michael Keller, with the pentahexes in an outer ring and the order 1 through 4 polyhexes in an inner ring; see the solution to the Hexnut inner ring): solutions incomplete
15x2 semi-regular hexagon: solutions incomplete
Triangle: solutions incomplete
17x15 trapezoid: solutions incomplete
18x12 trapezoid: solutions incomplete
32x5 trapezoid: solutions incomplete
One-Sided Polyhexes of Order 1 Through 5
These puzzles uses the monohex, the dihex, the three trihexes, the ten one-sided tetrahexes, and the 33 one-sided pentahexes, for a total of 217 hexagons.
Hexagon: solutions incomplete
31x7 parallelogram: solutions incomplete
22x14 trapezoid: solutions incomplete
Hexahexes
The 82 hexahexes total 492 hexagons.
Hexagon ring (design from Kadon's Hexnut II): solutions incomplete
