|Bowers style acronym||Tic|
|Coxeter diagram||x4x3o ()|
|Faces||8 triangles, 6 octagons|
|Vertex figure||Isosceles triangle, edge lengths 1, √, √ |
|Measures (edge length 1)|
|Number of external pieces||14|
|Level of complexity||3|
|Abstract & topological properties|
|Symmetry||B3, order 48|
The truncated cube, the truncated hexahedron, or tic, is one of the 13 Archimedean solids. It consists of 8 triangles and 6 octagons. Each vertex joins one triangle and two octagons. As the name suggests, it can be obtained by truncation of the cube.
Vertex coordinates[edit | edit source]
A truncated cube of edge length 1 has vertex coordinates given by all permutations of:
Representations[edit | edit source]
A truncated cube has the following Coxeter diagrams:
- x4x3o () (full symmetry)
- xwwx4xoox&#xt (BC2 axial, octagon-first)
- xwwxoo3ooxwwx&#xt (A2 axial, triangle-first)
- wx3oo3xw&#zx (A3 subsymmetry, as hull of 2 small rhombitetratetrahedra)
- wx xw4xo&#zx (BC2×A1 symmetry)
- wwx wxw xww&#zx (A1×A1×A1 symmetry)
- oxwUwxo xwwxwwx&#xt (A1×A1 axial)
Semi-uniform variant[edit | edit source]
With edges of length a (between two ditetragons) and b (between a ditetragon and a triangle), its circumradius is given by
and its volume is given by
It has coordinates given by all permutations of:
Related polyhedra[edit | edit source]
A truncated cube can be augmented by attaching a square cupola to one of its octagonal faces, forming the augmented truncated cube. If a second square cupola is attached to the opposite octagonal face, the result is the biaugmented truncated cube.
[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 2: Truncates" (#11).
- Klitzing, Richard. "tic".
- Quickfur. "The Truncated Cube".