# Hollow cuboid cupoliprism

Hollow cuboid cupoliprism
Rank4
TypeScaliform
SpaceSpherical
Notation
Bowers style acronymHocucup
Elements
Cells12 tetrahedra as 6 stella octangulae, 12 blends of 2 triangular prisms
Faces48 triangles, 24 squares
Edges24+48
Vertices24
Vertex figureFaceted wedge, edge lengths 1 (equilateral triangles' edges), 2 (pseudo-edge), 2 (other edges)
Measures (edge length 1)
Circumradius$\frac{\sqrt{10}}{4} ≈ 0.79057$ Height$\frac{\sqrt2}{2} ≈ 0.70711$ Related polytopes
ArmyCope
RegimentHocucup
ConjugateNone
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame

The hollow cubic cupoliprism or hocucup is a prismatic scaliform polychoron that consists of 6 stella octangulae (or 12 tetrahedra) and 12 blends of 2 triangular prisms. Each vertex is met by two tetrahedra and four blends of 2 triangular prisms.

This polychoron can be created as a blend of 6 tetrahedral prisms (in the form of 6 digonal antiduoprisms). In the process all the tetrahedra compound in pairs, while the triangular prisms blend in pairs at a square face. The object has cube prismatic symmetry and has the vertices of a scaled cuboctahedral prism.

It was first discovered and described by Polytope Discord user _Geometer on November 20, 2020.

## Vertex coordinates

The vertices of a hollow cubic cupoliprism of edge length 1 are given by all permutations of the first three coordinates of:

• $\left(±\frac12,\,±\frac12,\,0,\,±\frac{\sqrt2}{4}\right).$ 