Truncated tetrahedral prism
Jump to navigation
Jump to search
Truncated tetrahedral prism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Tuttip 
Coxeter diagram  x x3x3o () 
Elements  
Cells  4 triangular prisms, 4 hexagonal prisms, 2 truncated tetrahedra 
Faces  8 triangles, 6+12 squares, 8 hexagons 
Edges  12+12+24 
Vertices  24 
Vertex figure  Sphenoid, edge lengths 1, √3, √3 (base), √2 (legs) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Trip–4–hip: 
Tut–6–hip: 90°  
Tut–3–trip: 90°  
Hip–4–hip:  
Height  1 
Central density  1 
Number of external pieces  10 
Level of complexity  12 
Related polytopes  
Army  Tuttip 
Regiment  Tuttip 
Dual  Triakis tetrahedral tegum 
Conjugate  None 
Abstract & topological properties  
Flag count  576 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  A_{3}×A_{1}, order 48 
Convex  Yes 
Nature  Tame 
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 K4.57 on Richard Klitzing's list).
Gallery[edit  edit source]

Card with cell counts, verf, and crosssections

Segmentochoron display, tut atop tut

Net
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 (A_{2}×A_{1} symmetry, triangular prismfirst)
 x(xu)(xu)x3x(xo)(oo)o&#xr (A_{2} axial)
 xxxx xuxo oxux&#xt (A_{1}×A_{1}×A_{1} axial, squarefirst)
External links[edit  edit source]
 Bowers, Jonathan. "Category 19: Prisms" (#898).
 Klitzing, Richard. "Tuttip".
 Wikipedia contributors. "Truncated tetrahedral prism".