Elongated square bipyramid

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Elongated square bipyramid
Rank3
TypeCRF
Notation
Bowers style acronymEsquidpy
Coxeter diagramoxxo4oooo&#xt
Elements
Faces8 triangles, 4 squares
Edges4+8+8
Vertices2+8
Vertex figures2 squares, edge length 1
 8 kites, edge lengths 1 and 2
Measures (edge length 1)
Volume
Dihedral angles3–4:
 3–3:
 4–4: 90°
Central density1
Number of external pieces12
Level of complexity5
Related polytopes
ArmyEsquidpy
RegimentEsquidpy
DualSquare bifrustum
ConjugateNone
Abstract & topological properties
Flag count80
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryB2×A1, order 16
ConvexYes
NatureTame

The elongated square bipyramid is one of the 92 Johnson solids (J15). It consists of 8 triangles and 4 squares. It can be constructed by inserting a cube, seen as a square prism, between the two pyramidal halves of the regular octahedron, seen as a square bipyramid.

Vertex coordinates[edit | edit source]

An elongated square pyramid of edge length 1 has the following vertices:

  • ,
  • .

Representations[edit | edit source]

An elongated square bipyramid has the following Coxeter diagrams:

  • oxxo4oooo&#xt (full symmetry)
  • oxxo oxxo&#xt (rectangular symmetry)
  • xwx xox&#xt (rectangular axial)
  • wx ox4oo&#zx (as tegum sum)
  • x(xw)x o(qo)o&#xt (edge first)
  • qoo oqo xxw&#zx (cuboid symmetry)

External links[edit | edit source]