Pentagonal pyramidal prism

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Pentagonal pyramidal prism
Rank4
TypeSegmentotope
Notation
Bowers style acronymPeppyp
Coxeter diagramxx ox5oo&#x
Elements
Cells2 pentagonal pyramids, 5 triangular prisms, 1 pentagonal prism
Faces10 triangles, 10+10 squares, 2 pentagons
Edges1+5+10+10
Vertices2+10
Vertex figures2 pentagonal pyramids, edge lengths 1 (base) and 2 (legs)
 10 sphenoids, edge lengths 1 (2), 2 (3), and (1+5)/2 (1)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglestrip–4–trip:
 Peppy–3–trip: 90°
 Peppy–5–pip: 90°
 trip–4–pip:
HeightsPeppy atop peppy: 1
 Dyad atop pip:
Central density1
Related polytopes
ArmyPeppyp
RegimentPeppyp
DualPentagonal pyramidal tegum
ConjugatePentagrammic pyramidal prism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH2×A1×I, order 20
ConvexYes
NatureTame

The pentagonal pyramidal prism, or peppyp, is a CRF segmentochoron (designated K-4.38 on Richard Klitzing's list). It consists of 2 pentagonal pyramids, 1 pentagonal prism, and 5 triangular prisms.

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

Two pentagonal pyramidal prisms can be attached to the pentagonal prismatic cells of the pentagonal antiprismatic prism to produce the uniform icosahedral prism.

Vertex coordinates[edit | edit source]

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

Representations[edit | edit source]

A pentagonal pyramidal prism has the following Coxeter diagrams:

  • xx o54oo&#x (full symmetry)
  • oxxo5oooo&#xr (H2 axial only, pentagonal pyramid atop pentagonal pyramid)

External links[edit | edit source]