Quasitruncated hexahedron
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Quasitruncated hexahedron | |
---|---|
Rank | 3 |
Type | Uniform |
Space | Spherical |
Notation | |
Bowers style acronym | Quith |
Coxeter diagram | x4/3x3o () |
Elements | |
Faces | 8 triangles, 6 octagrams |
Edges | 12+24 |
Vertices | 24 |
Vertex figure | Isosceles triangle, edge lengths 1, √2–√2, √2–√2 |
Measures (edge length 1) | |
Circumradius | |
Volume | |
Dihedral angles | 8/3–8/3: 90° |
8/3–3: | |
Central density | 7 |
Number of external pieces | 54 |
Level of complexity | 11 |
Related polytopes | |
Army | Sirco, edge length |
Regiment | Quith |
Dual | Great triakis octahedron |
Conjugate | Truncated cube |
Convex core | Octahedron |
Abstract & topological properties | |
Flag count | 144 |
Euler characteristic | 2 |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | B_{3}, order 120 |
Convex | No |
Nature | Tame |
The quasitruncated hexahedron, the quasitruncated cube, or quith, also called the stellated truncated hexahedron, is a uniform polyhedron. It consists of 8 triangles and 6 octagrams. Each vertex joins one triangle and two octagrams. As the name suggests, it can be obtained by quasitruncation of the cube.
Vertex coordinates[edit | edit source]
A quasitruncated hexahedron of edge length 1 has vertex coordinates given by all permutations and sign changes of
Related polyhedra[edit | edit source]
The quasitruncated rhombihedron is a uniform polyhedron compound composed of 5 quasitruncated hexahedra.
Name | OBSA | Schläfli symbol | CD diagram | Picture |
---|---|---|---|---|
Cube | cube | {4/3,3} | x4/3o3o () | |
Quasitruncated hexahedron | quith | t{4/3,3} | x4/3x3o () | |
Cuboctahedron | co | r{3,4/3} | o4/3x3o () | |
Truncated octahedron | toe | t{3,4/3} | o4/3x3x () | |
Octahedron | oct | {3,4/3} | o4/3o3x () | |
Quasirhombicuboctahedron | querco | rr{3,4/3} | x4/3o3x () | |
Quasitruncated cuboctahedron | quitco | tr{3,4/3} | x4/3x3x () | |
(degenerate, oct+6(4)) | o4/3o3ß () | |||
Icosahedron | ike | s{3,4/3} | o4/3s3s () |
External links[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category 2: Truncates" (#17).
- Klitzing, Richard. "quith".
- Wikipedia Contributors. "Stellated truncated hexahedron".
- McCooey, David. "Stellated Truncated Hexahedron"