Pentagonal cupolic prism

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Pentagonal cupolic prism
Rank4
TypeSegmentotope
SpaceSpherical
Notation
Bowers style acronymPecupe
Coxeter diagramxx ox5xx&#x
Elements
Cells5 triangular prisms, 5 cubes, 1 pentagonal prism, 2 pentagonal cupolas, 1 decagonal prism
Faces10 triangles, 5+5+5+10+10 squares, 2 pentagons, 2 decagons
Edges5+10+10+10+10+20
Vertices10+20
Vertex figures10 isosceles trapezoidal pyramids, base edge lengths 1, 2, (1+5)/2, 2, side edge length 2
 20 irregular tetrahedra, edge lengths 1 (1), 2 (4), and (5+5)/2 (1)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTrip–4–cube:
 Cube–4–pip:
 Pecu–3–trip: 90°
 Pecu–4–cube: 90°
 Pecu–5–pip: 90°
 Pecu–10–dip: 90°
 Trip–4–dip:
 Cube–4–dip:
HeightsPecu atop pecu: 1
 Pip atop dip:
Central density1
Related polytopes
ArmyPecupe
RegimentPecupe
DualSemibisected pentagonal trapezohedral tegum
ConjugateRetrograde pentagrammic cupolic prism
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryH2×A1×I, order 20
ConvexYes
NatureTame


The pentagonal cupolic prism, or pecupe, is a CRF segmentochoron (designated K-4.117 on Richard Klitzing's list). It consiss of 2 pentagonal cupolas, 5 triangular prisms, 5 cubes, 1 pentagonal prism, and 1 decagonal prism.

As the name suggests, it is a prism based on the pentagonal cupola. As such, it is a segmentochoron between two pentagonal cupolas. It can also be viewed as a segmentochoron between a decagonal prism and a pentagonal prism.

It can be obtained as a segment of the small rhombicosidodecahedral prism.

Vertex coordinates[edit | edit source]

Coordinates of the vertices of a pentagonal cupolic prism of edge length 1 centered at the origin are given by:

External links[edit | edit source]