Retrograde pentagonal cuploid

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Retrograde pentagonal cuploid
Rank3
TypeSegmentotope
Notation
Bowers style acronymRapescu
Elements
Faces5 triangles, 5 squares, 1 pentagon
Edges5+5+10
Vertices5+5
Vertex figures5 isosceles trapezoids, edge lengths 1, 2, (1+5)/2, 2
 5 butterflies, edge lengths 1, 2, 1, 2
Measures (edge length 1)
Circumradius
Dihedral angles5–4:
 3–4:
Height
Related polytopes
ArmyPentagonal frustum
ConjugatePentagrammic cuploid
Abstract & topological properties
Euler characteristic1
OrientableNo
Genus1
Properties
SymmetryH2×I, order 10
ConvexNo
NatureTame

The retrograde pentagonal cuploid, also called the retrograde pentagonal semicupola or rapescu, is an orbiform polyhedron. It consists of 5 triangles, 5 squares, and 1 pentagon. It is a cuploid based on the pentagon seen as {5/4}, with a pseudo {10/4} base.

Vertex coordinates[edit | edit source]

A retrograde pentagonal cuploid of edge length 1 has vertices given by the following coordinates:

Related polyhedra[edit | edit source]

The retrograde pentagonal cuploid can be edge-inscribed into the small ditrigonary icosidodecahedron; it uses triangles and pentagons of the great ditrigonary icosidodecahedron as well as squares of the rhombihedron, the inscribed compound of 5 cubes.

External links[edit | edit source]