Cubic pyramid

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Cubic pyramid
Rank4
TypeSegmentotope
Notation
Bowers style acronymCubpy
Coxeter diagramox4oo3oo&#x
Tapertopic notation[111]1
Elements
Cells6 square pyramids, 1 cube
Faces12 triangles, 6 squares
Edges8+12
Vertices1+8
Vertex figures1 cube, edge length 1
 8 triangular pyramids, edge lengths 2 (base) and 1 (sides)
Measures (edge length 1)
Circumradius1
Hypervolume
Dichoral anglesSquippy–3–squippy: 120°
 Squippy–4–cube: 45°
HeightsPoint atop cube:
 Square atop squippy:
Central density1
Related polytopes
ArmyCubpy
RegimentCubpy
DualOctahedral pyramid
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB3×I, order 48
ConvexYes
NatureTame

The cubical pyramid, or cubpy, is a CRF segmentochoron (designated K-4.26 on Richard Klitzing's list). It has 6 square pyramids and 1 cube as cells. As the name suggests, it is a pyramid based on the cube.

The cubic pyramid occurs as a vertex-first cap of the regular icositetrachoron.

A regular tesseract can be exactly decomposed into 8 CRF cubic pyramids.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a cubic pyramid of edge length 1 are given by:

Representations[edit | edit source]

A cubic pyramid has the following Coxeter diagrams:

  • ox4oo3oo&#x (full symmetry)
  • ox ox4oo&#x (BC2×A1 base, square prismatic pyramid)
  • ox ox ox&#x (A1×A1×A1 base, cuboid pyramid)
  • oxx4ooo&#x (base square atop square)
  • oxx oxx&#x (*similar with rectangles)

External links[edit | edit source]