Hollow cuboid cupoliprism

Hollow cuboid cupoliprism
Rank	4
Type	Scaliform
Space	Spherical
Notation
Bowers style acronym	Hocucup
Elements
Cells	12 tetrahedra as 6 stella octangulae, 12 blends of 2 triangular prisms
Faces	48 triangles, 24 squares
Edges	24+48
Vertices	24
Vertex figure	Faceted 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
Army	Cope
Regiment	Hocucup
Conjugate	None
Properties
Symmetry	B3×A1, order 96
Convex	No
Nature	Tame

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:

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

External links

• Klitzing, Richard. "Hocucup".

• Bowers, Jonathan. "Category S1: Simple Scaliforms" (#S6).