Triangular-tetrahedral duoprismatic prism

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Triangular-tetrahedral duoprismatic prism
Rank6
TypeUniform
Notation
Bowers style acronymTratepe
Coxeter diagramx x3o x3o3o ()
Tapertopic notation12111
Elements
Peta2 triangular-tetrahedral duoprisms, 3 square-tetrahedral duoprisms, 4 triangular duoprismatic prisms
Tera3+6 tetrahedral prisms, 8 triangular duoprisms, 6+12 triangular-square duoprisms
Cells6 tetrahedra, 4+12+12+24 triangular prisms, 18 cubes
Faces8+24 triangles, 12+18+36 squares
Edges12+24+36
Vertices24
Vertex figureTriangular scalenic pyramid, edge lengths 1 (base triangle and top edge of base) and 2 (remaining edges)
Measures (edge length 1)
Circumradius
Hypervolume
Dipetal anglesTratet–tepe–squatet: 90°
 Tratet–triddip–tratrip: 90°
 Squatet–tisdip–tratrip: 90°
 Tratrip–tisdip–tratrip:
 Squatet–tepe–squatet: 60°
HeightsTratet atop tratet: 1
 Tepe atop squatet:
 Trip atop tratrip:
 Tisdip atop ortho tisdip:
Central density1
Number of external pieces9
Level of complexity60
Related polytopes
ArmyTratepe
RegimentTratepe
DualTriangular-tetrahedral duotegmatic tegum
ConjugateNone
Abstract & topological properties
Flag count17280
Euler characteristic0
OrientableYes
Properties
SymmetryA3×A2×A1, order 288
ConvexYes
NatureTame

The triangular-tetrahedral duoprismatic prism or tratepe is a convex uniform duoprism that consists of 2 triangular-tetrahedral duoprisms, 3 square-tetrahedral duoprisms, and 4 triangular duoprismatic prisms. Each vertex joins 1 triangular-tetrahedral duoprism, 2 square-tetrahedral duoprisms, and 3 triangular duoprismatic prisms. As the name suggests, it is a prism based on the triangular-tetrahedral duoprism, which also makes it a convex segmentopeton.

Vertex coordinates[edit | edit source]

The vertices of a triangular-tetrahedral duoprismatic prism of edge length 1 are given by all even sign changes of the last three coordinates of:

External links[edit | edit source]