Truncated tetrahedral prism
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|Truncated tetrahedral prism|
|Bowers style acronym||Tuttip|
|Coxeter diagram||x x3x3o ()|
|Cells||4 triangular prisms, 4 hexagonal prisms, 2 truncated tetrahedra|
|Faces||8 triangles, 6+12 squares, 8 hexagons|
|Vertex figure||Sphenoid, edge lengths 1, √3, √3 (base), √2 (legs)|
|Measures (edge length 1)|
|Number of pieces||10|
|Level of complexity||12|
|Dual||Triakis tetrahedral tegum|
|Symmetry||A3×A1, order 48|
The truncated tetrahedral prism or tuttip is a prismatic uniform polychoron that consists of 2 truncated tetrahedra, 4 hexagonal prisms, and 4 triangular prisms. Each vertex joins 1 truncated tetrahedron, 1 triangular prism, and 2 hexagonal prisms. As the name suggests, it is a prism based on the truncated tetrahedron. As such it is also a convex segmentochoron (designated K-4.57 on Richard Klitzing's list).
Gallery[edit | edit source]
Card with cell counts, verf, and cross-sections
Segmentochoron display, tut atop tut
Vertex coordinates[edit | edit source]
Coordinates for the vertices of a truncated tetrahedral prism of edge length 1 are given by all permutations and even sign changes of the first three coordinates of:
Representations[edit | edit source]
A truncated tetrahedral prism has the following Coxeter diagrams:
- x x3x3o (full symmetry)
- xx3xx3oo&#x (bases considered separately)
- x2s4o3x () (bases as snub)
- xxx xux3oox&#xt (A2×A1 symmetry, triangular prism-first)
- x(xu)(xu)x-3-x(xo)(oo)o-&#xr (A2 axial)
- xxxx xuxo oxux&#xt (A1×A1×A1 axial, square-first)
External links[edit | edit source]
- Bowers, Jonathan. "Category 19: Prisms" (#898).
- Klitzing, Richard. "Tuttip".
- Wikipedia Contributors. "Truncated tetrahedral prism".