The Puzzling World of Polyhedral Dissections
By Stewart T. Coffin

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Tables

Figure Chapter Description
1 Introduction Blocks and Pins - Introductory graphic
2 Introduction Burrs
3 Introduction The Platonic Solids
4 Introduction Wood puzzle from Johnson Smith & Co. 1930s Catalog
5 1 Spherical jigsaw puzzle
6a 1 Tangram puzzle from Richter and Co.
6b 1 Tangram candy dishes from 1860s China
7 1 Tangram design grid
8 1 Tangram design possibilities
9 1 Tangram sample patterns
10 1 Tangram convex patterns
11 1 Tangram puzzling pairs
12 1 Dissection grids
13 1 Tangram with large triangles omitted
14 1 Other Richter and Co. rectangular puzzle patterns
15 1 Other Richter and Co. polygonal puzzle patterns
16 1 Other Richter and Co. puzzle patterns with complicated angles
17 1 Loculus of Archimedes
18 1 Allan Boardman's miniature Tangram set
19 1 Sam Loyd's square dissection puzzle
20 1 Sam Loyd's square dissection puzzle - Patterns possible with modified piece
21 1 Henry Dudeney's four-piece dissection
22 1 Typical 12-piece checkerboard dissection
23 2 Possible ways to tile the plane
24 2 Ways to join triangles through size-six
25 2 Patterns for assembling pieces from Fig. 24
26 2 Ways to join two-block rhombuses
27 2 Possible patterns for pieces from Fig. 26
28 2 Ways to join squares through size-six (polyominoes)
29 2 Showing how a 4 x 5 rectangle cannot be assembled from size-four polyominoes
30 2 Size-four polyominoes with checkering
31 2 Pentomino pieces
32 2 Pentominoes solutions for 3 x 20, 4 x 15, 5 x 12 and 6 x 10
33 2 Pentominoes by Wayne Daniel
34 2 Pentominoes analysis technique
35 2 Checkerboard puzzle pieces from Canterbury Puzzles
36 2 Checkerboard puzzle
37 2 Cornucopia Puzzle pieces
37a 2 Cornucopia Puzzle by Stewart Coffin
38 2 Cornucopia Puzzle 8 x 8 fourfold symmetry patterns
39 2 Cornucopia Puzzle 3 x 20 impossibility proof
40 2 Cornucopia Puzzle pieces
41 2 Two Cornucopia Puzzle patterns
42 2 One "obscene" Cornucopia Puzzle pattern
43a 2 Symmetry illustration 1
43b 2 Symmetry illustration 2
43c 2 Symmetry illustration 3
44 2 Ways to join hexagons through size-four (hexominoes)
45 2 Hexagonal cluster patterns
46a 2 Snowflake Puzzle - Hexagon solution
46b 2 Snowflake Puzzle - Snowflake solution
46c 2 Snowflake Puzzle by Stewart Coffin
47 2 Snowflake Puzzle patterns
48 3 Diabolical Cube pieces
49 3 Mikusinski's Cube pieces
50a 3 Soma Cube pieces
50b 3 Soma Cube by Trevor Wood
51 3 Four-piece, serially-interlocking 3 x 3 x 3 cube
52 3 Ways to join four or five cubes
53 3 Half Hour Puzzle pieces
54 3 Other patterns from Half Hour Puzzle pieces
55 3 One example of five-piece 3 x 3 x 3 cube with all non-symmetrical pieces
56 3 Solid Pentomino Puzzle pieces
57 3 Solid Pentominoes by Trevor Wood
58 3 Pentacube pieces
59 3 Checkered Pentacube 5 x 5 x 2
60 3 Joined 1 x 2 x 2 block pieces
61a 4 Convolution Puzzle pieces
61b 4 Convolution Puzzle by Stewart Coffin
61c 4 Convolution Puzzle by Wayne Daniel
62 4 Three-Piece Block Puzzle pieces
63 5 Interlocking box
64 5 Six-Piece Burr
65 5 Six-Piece Burr piece showing 12 cubic units that are possible to remove
66 5 Six-Piece Burr illustration of notchable and unnotchable pieces
67 5 Six-Piece Burr notchable pieces
68 5 Burr No. 305
69 5 Burr No. 306
70 5 Bill's Baffling Burr
71 5 Peter Marineau's level-nine burr
72 6 Illustration of homogeneity or congruence for burrs
73 6 Twelve-Piece and Three-Piece Burr
74 6 Twelve-Piece and Eighteen-Piece Burrs
75a 6 Altekruse Burr and piece
75b 6 Altekruse Burr by Tom Lensch
76 6 Altekruse Burr piece variations
77 6 Altekruse Burr unusual variation
78 6 Altekruse Burr variations with 24, 36 or 38 pieces
79 6 Altekruse Burr variation with pins and holes
80 6 Pin-Hole Puzzle and pieces
81 6 Pin-Hole Puzzle variations
82a 6 Corner Block Puzzle
82b 6 Corner Block Puzzle pieces
83 6 Twenty-Four Piece Burr
84 6 Twenty-Four Piece Burr - Other assemblies
85 7 Diagonal Burr pieces
86 7 Diagonal Burr mirror-image halves
87 7 Diagonal Burr with more than 100 pieces
88 7 Diagonal Burr with beveled pieces (Diagonal Star)
89 7 Diagonal Star piece components
90 7 Jig for making six-sided center blocks
91 8 Solids that fill the center of symmetrical stick arrangements
92a 8 Rhombic dodecahedron as a beveled cube
92b 8 Symmetry of rhombic dodecahedron
93 8 Cluster of 12 triangular sticks
94 8 Pin-Hole Puzzle - Theory of interlock illustration
95 8 Six-Piece Burr - Theory of interlock illustration
96 8 Diagonal Star - Theory of interlock illustration
97 8 One way to make the cluster of 12 triangular sticks interlocking
98 8 Third Stellation from the cluster of 12 triangular sticks
99 8 First Stellation from the second stellation from the cluster of 12 triangular sticks
100 8 The Second Stellation Puzzle foundation and piece
101 8 The Second Stellation Puzzle and piece
102 8 Four Corners Puzzle and piece
103 8 Four Corners Puzzle with color symmetry
104 8 Four Corners Puzzle with color symmetry assemblies
105 8 The Second Stellation Puzzle with color symmetry
106 8 The Second Stellation Puzzle with color symmetry assemblies
107a 8 The Third Stellation Puzzle with color symmetry
107b 8 The Third Stellation Puzzle with color symmetry - One assembly
108 9 The Permutated Second Stellation Puzzle and pieces
109 9 The Permutated Third Stellation Puzzle and pieces
110 9 The Broken Sticks Puzzle and pieces
111 9 The Augmented Second Stellation Puzzle and pieces
112 9 Puzzle building blocks
113 9 Rhombic dodecahedron dissection
114 9 Augmented Four Corners Puzzle and pieces
115 9 Diagonal Cube Puzzle and pieces
116 9 The Reluctant Cluster Puzzle and pieces
117 10

The Hexagonal Prism Puzzle and pieces

118 10

The Triangular Prism Puzzle and pieces

119 10 The Star Prism Puzzle (The General)
120 10 Other possible extensions to the prism family
121 10 The Square Prism Puzzle and piece
122 10 The Three Pairs Puzzle and pieces
123a 11 The Star of David Puzzle pieces and assembly patterns
123b 11 The Star of David Puzzle
124a 11 A Puzzle In Reverse (Triumph) - Assembly 1
124b 11 A Puzzle In Reverse (Triumph) - Assembly 2
124c 11 A Puzzle In Reverse (Triumph) - Assembly 3
125 12 Coordinate motion illustration
126 12 The Expanding Box Puzzle
127a 12 The Rosebud Puzzle pieces
127b 12 The Rosebud Puzzle assembled
127c 12 The Rosebud Puzzle assembled and expanded into a "bloom"
128 13 Cluster of 12 pinned hexagonal sticks (Locked Nest)
129 13 Cluster of 12 pinned hexagonal sticks (Locked Nest) pieces
130a 13 Cluster of 12 pinned hexagonal sticks (Locked Nest) extended
130b 13 Cluster of 12 pinned hexagonal sticks (Locked Nest) sub-unit
131 13 Pinned hexagonal sticks - Piece suggestions
132 13 The Cuckoo Nest Puzzle
133a 13 Triple Decker Puzzle (Nine Bars)
133b 13 Triple Decker Puzzle (Nine Bars) pieces
134 13 A Holey Hex Hybrid
135a 13 Hectix
135b 13 Hectix pieces
136 13 Notched Rhombic Sticks
137 14 Scorpius Puzzle
138 14 Scorpius Puzzle - Four-color assemblies
139 14 The Dislocated Scorpius Puzzle piece
140a 14 The Scrambled Scorpius Puzzle pieces
140b 14 The Scrambled Scorpius Puzzle
141 15 Dissected Rhombic Dodecahedra (Garnet Puzzle) and pieces
142 15 Jig for making Dissected Rhombic Dodecahedra pieces
143 15 Dissected Rhombic Dodecahedra (Garnet Puzzle) modified into other shapes
144a 15 Dissected Rhombic Dodecahedra (Split Star Puzzle) pieces
144b 15 Dissected Rhombic Dodecahedra (Split Star Puzzle)
145 15 The Pennyhedron Puzzle
146 15 The Pennyhedron Puzzle - Modifications
147 15 The Pennyhedron Puzzle - Modifications
148 16 The Pseudo-Notched Sticks Puzzle
149 16 The Square Face Puzzle
150 16 The Queer Gear and pieces
151 17 Thirty-faced triacontahedron
152 17 Thirty Pentagonal Sticks and Dowels
153 17 Pentagonal sticks - Cutting and drilling illustrations
154 17 Pentagonal Sub-Units
155 17 Notched Pentagonal Sticks
156a 17

Notched Rhombic Sticks piece

156b 17

Notched Rhombic Sticks

156c 17 Square-Rod Dodecaplex
157 17 The Jupiter Puzzle and piece
158 17 The Jupiter Puzzle showing color symmetry
159 17 The Dislocated Jupiter Puzzle piece only
160 17 A Scrambled Jupiter (compromise) pieces
161 17 The Jupiter Puzzle family - Piece specifications
162 17 The Dissected Triacontahedron
163 17 The Dissected Triacontahedron - Piece specifications
164 18 Truncated octahedra - Making from cubes
165 18 Ways to join truncated octahedra
166 18 The Setting Hen Puzzle
167 18 Ways to join rhombic dodecahedra through size-four
168 18 Rhombic dodecahedra patterns with isometric symmetry
169 18 The Leftover Block Puzzle pieces
170 18 Substitution of spheres in the rhombic dodecahedra pieces
171 18 The Four-Piece Pyramid Puzzle
172 18 The Octahedral Cluster Puzzle
173a 19 Abstraction and reality illustration 1
173b 19 Abstraction and reality illustration 2
174 20 The Two Tiers Puzzle
175 21 The Six-Part Invention pieces
176a 21 The Six-Part Invention (The Peanut Puzzle) patterns
176b 21 The Six-Part Invention (The Peanut Puzzle)
177 21 The Six-Part Invention (The Peanut Puzzle) additional patterns
178 21 The Eight-Piece Cube Puzzle (Pieces of Eight) pieces
179a 21 The Eight-Piece Cube Puzzle (Pieces of Eight) patterns
179b 21 The Eight-Piece Cube Puzzle (Pieces of Eight)
180 21 The Six-Part Invention pieces with 3 prongs
181 21 The Eight-Piece Cube Puzzle (Pieces of Eight) truncated pieces
182 21 Triple Cross Puzzle and piece
183 21 The Eight-Piece Cube Puzzle (Pieces of Eight) other piece variation
184 21 The Pillars of Hercules pieces from cubes
185 21 The Pillars of Hercules pieces from rhombic dodecahedra
186 22 Blocks and Pins example
187 22 Blocks and Pins from edge-beveled cubes and additional holes
188 22 Blocks and Pins from truncated cubes and additional holes
189 22 Blocks and Pins from rhombicuboctahedron blocks
190 22 Blocks and Pins - Pieces from edge-beveled cubes with only 12 holes
191 22 Pin-Hole Puzzle variation
192 22 Cubes with three mutually perpendicular non-intersecting holes
193 22 Cubes with three mutually perpendicular non-intersecting holes - Assembly
194 22 Cubes (2 x 2 x 2) with three non-intersecting holes with isometric symmetry
195 22 Dissection of Fig. 194
196 22 Assemblies from cubes in Fig. 194
197 22 Squat octahedra substituted for cubes in Fig. 194
198 22 Illustration of similarity between Fig. 128 and Fig. 197
199 22 Dissection of stellated rhombic dodecahedron with dowels
200 22 Individual piece from Fig. 199 with dowel fastened into place
201 22 The Lollipop Puzzle - Piece from Fig. 200 assembled into a tetrahedral pile
202 22 Triangular assembly of 3 pieces from Fig. 200.
203 22 Octahedral cluster assembly from six blocks
204 22 Showing the dowel diameter limit
205 22 Exceeding the limitation shown in Fig. 204 by milling the dowels
206 23 Jig for sawing square sticks
207 23 Jig for sawing rhombic dodecahedral blocks
208 23 Jig for sawing truncated octahedra
209 23 Jig for notching burr pieces
210 23 Jig for sawing equilateral-triangular sticks
211 23 Jigs for gluing First, Second and Third Stellation Puzzles
212 23 Gluing the Jupiter Puzzle
213 Finale Closing graphic

Table Chapter  
1 2 Polyiamond Piece Summary
2 2 Polyomino Piece Summary
3 2 Cornucopia Solution Summary
4 2 Hexagonal Piece Summary
5 17 Dissected Triacontahedron Piece Summary

 

1990-2012 by Stewart T. Coffin
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