Triangular-pentachoric duoprismatic prism

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Triangular-pentachoric duoprismatic prism
Rank7
TypeUniform
Notation
Bowers style acronymTrippen
Coxeter diagramx x3o x3o3o3o ()
Tapertopic notation13111
Elements
Exa2 triangular-pentachoric duoprisms, 3 square-pentachoric duoprisms, 5 triangular-tetrahedral duoprismatic prisms
Peta3+6 pentachoric prisms, 10 triangular-tetrahedral duoprisms, 15 square-tetrahedral duoprisms, 10 triangular duoprismatic prisms
Tera6 pentachora, 15+30 tetrahedral prisms, 20 triangular duoprisms, 10+30 triangular-square duoprisms
Cells30 tetrahedra, 5+20+30+60 triangular prisms, 30 cubes
Faces10+60 triangles, 15+30+60 squares
Edges15+30+60
Vertices30
Vertex figureTetrahedral scalenic pyramid, edge lengths 1 (base tetrahedron and top edge of base) and 2 (remaining edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diexal anglesTrapen–penp–squapen: 90°
 Trapen–tratet–tratepe: 90°
 Squapen–squatet–tratepe: 90°
 Tratepe–tratrip–tratepe:
 Squapen–penp–squapen: 60°
HeightsTrapen atop trapen: 1
 Penp atop squapen:
 Trip atop tratepe:
Central density1
Number of external pieces10
Level of complexity105
Related polytopes
ArmyTrippen
RegimentTrippen
DualTriangular-pentachoric duotegmatic tegum
ConjugateNone
Abstract & topological properties
Flag count151200
Euler characteristic2
OrientableYes
Properties
SymmetryA4×A2×A1, order 1440
ConvexYes
NatureTame

The triangular-pentachoric duoprismatic prism or trippen is a convex uniform duoprism that consists of 2 triangular-pentachoric duoprisms, 3 square-pentachoric duoprisms, and 5 triangular-tetrahedral duoprismatic prisms. Each vertex joins 1 triangular-pentachoric duoprism, 2 square-pentachoric duoprisms, and 4 triangular-tetrahedral duoprismatic prisms. As the name suggests, it is a prism based on the triangular-pentachoric duoprism, which also makes it a convex segmentoexon.

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