Truncated Trickery

Truncated Trickery
A catalog of all regular tilings of three dimensional space by the tetrahedron-cube-octahedron symmetry family.
An in-depth explanation of these vrml files can be found here.

by mattt chisholm and Jeremy Avnet

This page uses the table cell color tag, and only works under Netscape 3.x. If you don't see any colors in the table below, click here ->AA<- to open "vrml2.html" in this directory, or get Netscape 3.1.

Color key to reading the chart:

Any color: A single regular polyhedron. Each polyhedron is identified by it's own color.
White: A tiling, produced by combining the polyhedron at the top of the column and the polyhedron at the far left of the column.
Black: A heading, denoting which polygon (i.e. the type of face ) that the polyhedrons are meeting on.

Stay tuned! An in-depth explanation of this organizational strategy is coming soon...

Triangular Faces		Tetrahedral Symmetry
Triangular Faces		Tetrahedron	Truncated Cube	Cubctahedron
Octahedral Symmetry	Octahedron	Tetrahedron & Octahedron	Octahedron & Truncated Cube	Octahedron & Cuboctahedron
	Truncated Tetrahedron	Tetrahedron & Truncated Tetrahedron	Tetrahedron & Truncated Tetrahedron	Truncated Tetrahedron, Truncated Octahedron, & Cuboctahedron
	Double Truncated Cube	Tetrahedron, Cube, & Double Truncated Cube	Cube, Truncated Cube, Double Truncated Cube, & Octagonal Prism	Cube, Cuboctahdron & Double Truncated Cube

Square Faces

Square Orientation	Cube	Double Truncated Cube
Double Truncated Cube	Cube, Truncated Cube, Double Truncated Cube, & Octagonal Prism	Cube, Cuboctahedron, & Double Truncated Cube
Cube	Cube	Same as above left

Diamond Orientation	Cube	Truncated Octahedron	Cubctahedron
Cubctahedron	Cube, Cuboctahedron, & Double Truncated Cube	Truncated Tetrahedron, Truncated Octahedron, & Cuboctahedron	Octahedron & Cuboctahedron
Truncated Octahedron	Cube, Truncated Octahedron, & Double Truncated Octahedron	Truncated Octahedron	Same as above left
Cube	Not applicable	Same as above left	Same as first cell

Double Truncated Orientation	Cube	Double Truncated Cube	Double Truncated Octahedron
Double Truncated Octahedron	Cube, Truncated Cube, & Double Truncated Octahedron	Cube, Double Truncated Cube, Double Truncated Octahedron, & Octagonal Prism	Truncated Tetrahedron, Truncated Cube, and Double Truncated Octahedron
Double Truncated Cube	Cube, Cuboctahedron, & Double Truncated Cube	Tetrahedron, Cube & Double Truncated Cube	Same as above left
Cube	Not applicable	Same as above left	Same as first cell

Hexagonal Faces	Truncated Tetrahedron	Truncated Octahedron	Double Truncated Octahedron
Double Truncated Octahedron	Truncated Tetrahedron, Truncated Cube, & Double Truncated Octahedron	Cube, Truncated Octahedron, & Double Truncated Octahedron	Double Truncated Octahedron & Octagonal Prism
Truncated Octahedron	Truncated Tetrahedron, Truncated Octahedron, & Cuboctahedron	Truncated Octahedron	Same as above left
Truncated Tetrahedron	Tetrahedron & Truncated Tetrahedron	Same as above left	Same as first cell

Octagonal Faces	Truncated Cube	Double Truncated Octahedron
Double Truncated Octahedron	Truncated Tetrahedron, Truncated Cube, & Double Truncated Octahedron	Cube, Truncated Octahedron, and Double Truncated Octahedron
Truncated Cube	Octahedron & Truncated Cube	Same as first cell

Other geometric VRML eye toys:

Isometric Projection Of The Hypercube In Three Dimensions
spz szp psz pzs zsp zps
Rhombic Dodecahedron

May 13, 1997