Retrocelliprismatotruncatododecateron

Retrocelliprismatotruncatododecateron
Rank5
TypeUniform
Notation
Bowers style acronymRecaptid
Coxeter diagramx3x3x3x *b3/2o3*c ()
Elements
Tera30 truncated tetrahedral prisms, 12 prismatotrispentachora, 6 great prismatodecachora
Cells120 triangular prisms, 120 hexagonal prisms, 60 truncated tetrahedra, 30 octahemioctahedra, 60 truncated octahedra
Faces240 triangles, 90+360 squares, 120+240 hexagons
Edges360+720
Vertices360
Vertex figureBowtie scalene, base edge lengths 1 and 3, remaining edge lengths 2 (5) and 3 (4)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {5}}\approx 2.23608}$
Hypervolume${\displaystyle {\frac {381{\sqrt {3}}}{10}}\approx 65.99114}$
Diteral anglesPittip–tut–tuttip: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{5}}\right)\approx 129.23152^{\circ }}$
Pittip–oho–pittip: ${\displaystyle \arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }}$
Pittip–trip–tuttip: ${\displaystyle \arccos \left(-{\frac {\sqrt {10}}{10}}\right)\approx 108.43495^{\circ }}$
Pittip–toe–gippid: ${\displaystyle \arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }}$
Gippid–hip–tuttip: ${\displaystyle \arccos \left({\frac {\sqrt {10}}{10}}\right)\approx 71.56505^{\circ }}$
Related polytopes
ArmyCaptid
RegimentCaptid
ConjugateNone
Abstract & topological properties
Flag count57600
OrientableYes
Properties
SymmetryA5×2, order 1440\
ConvexNo
NatureTame

The retrocelliprismatotruncatododecateron, or recaptid, is a nonconvex uniform polyteron. It consists of 12 prismatotrispentachora, 30 truncated tetrahedral prisms, and 6 central great prismatodecachora. 2 prismatotrispentachora, 2 truncated tetrahedral prisms, and 2 great prismatodecachora join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the celliprismatotruncatododecateron.