Chapter 2 - Polyhedra

Chapter 2 includes a table of some of the convex polyhedra that he used either as hulls or to make the tunnels that drill through the hulls, or joined them together to make rings. This is a very handy reference, especially noting the nomenclature by which he refers to these figures. I have reproduced this table, and added the other Johnson solids that he used in the book, but did not include in his original table. I have also added the named non-convex figures that he used in construction, such as G3, and Z4.

After the table is the page by page listings of all the models in this chapter.

Platonic Solids 333 Y3 Tetrahedron p.227 444 P4 Cube p.49 3333 S3 Octahedron p.51 555 D5 Dodecahedron p.56 33333 I5 Icosahedron p.55 Archimedean Solids 366 T3 Truncated Tetrahedron p.34 388 T4 Truncated Cube p.5 3 10 10 T5 Truncated Dodecahedron p.171 3434 B4 Cuboctahedron p.33 3535 B5 Icosidodecahedron p.183 566 C5 Truncated Icosahedron p.164 466 K3 Truncated Octahedron p.34 468 K4 Truncated Cuboctahedron p.94 4 6 10 K5 Truncated Icosidodecahedron p.185 3444 E4 Rhombicuboctahedron p.94 3454 E5 Rhombicosidodecahedron p.138 43333 sB4 Snub Cuboctahedron p.228 53333 sB5 Snub Icosidodecahedron   Prisms and Antiprisms 44n Pn n-gonal Prism, n >= 3 p.1 333n Sn n-gonal Antiprism, n >= 3 p.222 Non-Convex Creations G3 G3 G3 p.129 Z4 Z4 Z4 p.132 X X X p.134 A5 A5 A5 p.154 A5' A5' A5' p.155 A5" A5" A5" p.156 m m m p.156 m* m* m* p.157

Johnson Solids J01 Y4 Square Pyramid p.225 J02 Y5 Pentagonal Pyramid p.224 J03 Q3 Triangular Cupola p.226 J04 Q4 Square Cupola p.225 J05 Q5 Pentagonal Cupola p.221 J06 R5 Pentagonal Rotunda p.222 J11 J11 Gyroelongated Pentagonal Pyramid aka Aug.S5 aka Dim.I5 p.139 J12 J12 Triangular Dipyramid p.26 J13 J13 Pentagonal Dipyramid p.26 J17 J17 Gyroelongated Square Dipyramid p.26 J37 J37 Elongated Square Gyrobicupola p.17 J38 J38 Elongated Pentagonal Orthobicupola p.87 J39 J39 Elongated Pentagonal Gyrobicupola p.87 J40 J40 Elongated Pentagonal Orthocupolarotunda p.87 J41 J41 Elongated Pentagonal Gyrocupolarotunda p.87 J42 J42 Elongated Pentagonal Orthobirotunda p.87 J43 J43 Elongated Pentagonal Gyrobirotunda p.87 J51 J51 Triaugmented Triangular Prism p.26 J62 J62 Metabidiminished Icosahedron p.139 J63 J63 Tridiminished Icosahedron p.132 J68 J68 Augmented Truncated Dodecahedron p.147, 181 J69 J69 Para Biaugmented Truncated Dodecahedron p.181 J70 J70 Meta Biaugmented Truncated Dodecahedron p.181 J71 J71 Triaugmented Truncated Dodecahedron p.181 J72 J72 Gyrate Rhombicosidodecahedron p.138, 143 J73 J73 Parabigyrate Rhombicosidodecahedron p.138, 143 J74 J74 Metabigyrate Rhombicosidodecahedron p.143 J75 J75 Trigyrate Rhombicosidodecahedron p.143 J76 J76 Diminished Rhombicosidodecahedron p.143 J77 J77 Paragyrate Diminished Rhombicosidodecahedron p.143 J78 J78 Metagyrate Diminished Rhombicosidodecahedron p.143 J79 J79 Bigyrate Diminished Rhombicosidodecahedron p.143 J80 J80 Parabidiminished Rhombicosidodecahedron p.143 J81 J81 Metabidiminished Rhombicosidodecahedron p.143 J82 J82 Gyrate Bidiminished Rhombicosidodecahedron p.143 J83 J83 Tridiminished Rhombicosidodecahedron p.137, 143 J84 J84 Snub Disphenoid - Siamese Dodecahedron p.26 J85 J85 Snub Square Antiprism p.160 J91 J91 Bilunabirotunda p.126 J92 J92 Hebesphenorotunda p.166

The following is a page-by-page listing of the remaining models from this chapter:

Model	.Stel	Genus	Properties	Pages with Diagram	Pages with Description	Notes
S3*	.Stel	q=1	(R)(A)(Q)	11		non-orientable - aka tetrahemihexahedron
S3*S3S3*S3S3*S3S3*S3S3*	.Stel	q=5	(R)(A)	12		non-orientable
B4,4	.Stel	q=4	(R)(A)(Q)	13	12	non-orientable - aka cubohemioctahedron
B4,3	.Stel	p=1	(R)(A)(Q)	13	12	orientable self-intersecting faces - aka octahemioctahedron
B5,5	.Stel	q=14	(R)(A)(Q)		13	non-orientable - aka small dodecahemidodecahedron
B5,3	.Stel	q=6	(R)(A)(Q)		13	non-orientable - aka small icosihemidodecahedron
E4*	.Stel	q=8	(R)(A)(Q)		13	non-orientable - aka small rhombihexahedron
E4**	.Stel	p=3	(R)(A)(Q)		13	orientable self-intersecting faces - aka small cubicuboctahedron
E5*	.Stel	q=20	(R)(A)(Q)		13	non-orientable - aka small rhombidodecahedron
E5**	.Stel	p=9	(R)(A)(Q)		13	orientable self-intersecting faces - aka small dodecicosidodecahedron
Q3gQ3 / gQ3Q3	.Stel	1	(R)(A)	18		orientable self-intersecting faces

Prev - Chapter 1 - Introduction and Dedication
Next - Chapter 3 - Cardboard, Rubber Band Method
Back to Adventures Among the Toroids - Index

Disclaimer: These pages are dedicated to B.M. Stewart. They are intended to be used by readers of his book to better illustrate his ideas in three dimensions. His book has tons of information that I do not intend to represent here, and I highly encourage anyone interested in this subject to buy the book. If you like my illustrations, please let me know. And if you are interested in a particular Stewart Toroid being modeled, please let me know and I will do what I can.

Thanks also to Robert Webb for his very cool "Stella" program. I have used it extensively to generate VRML files for my site. It is a great tool for rapid exploration of augmentations and excavations of polyhedra (among other things).

Alexander's Polyhedra, (c) 1998-2006, Alex Doskey