# Gyroelongated square bipyramid

Gyroelongated square bipyramid Rank3
TypeCRF
SpaceSpherical
Notation
Bowers style acronymGyesqidpy
Coxeter diagramoxoo4ooxo&#xt
Elements
Faces8+8 triangles
Edges8+8+8
Vertices2+8
Vertex figures2 squares, edge length 1
8 pentagons, edge length 1
Measures (edge length 1)
Volume$\frac{\sqrt2+\sqrt{4+3\sqrt2}}{3} ≈ 1.42840$ Dihedral angles3–3 join: $\arccos\left(\frac{1-\sqrt2-2\sqrt{2}}{3}\right) ≈ 158.57177°$ 3–3 antiprismatic: $\arccos\left(\frac{2\sqrt2-1}{3}\right) ≈ 127.55160°$ 3–3 pyramidal: $\arccos\left(-\frac13\right) ≈ 109.47122°$ Central density1
Related polytopes
ArmyGyesqidpy
RegimentGyesqidpy
DualOrder-4 truncated tetragonal trapezohedron
ConjugateGyroelongated square bipyramid
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(I2(8)×A1)/2, order 16
ConvexYes
NatureTame

The gyroelongated square bipyramid is one of the 92 Johnson solids (J17). It consists of 8+8 triangles as faces. It can be constructed by inserting a square antiprism between the two pyramidal halves of the regular octahedron, seen as a square bipyramid.

## Vertex coordinates

A gyroelongated square bipyramid of edge length 1 has the following vertices:

• $\left(0,\,0,\,±\frac{2\sqrt2+\sqrt{8}}{4}\right),$ • $\left(±\frac12,\,±\frac12,\,\frac{\sqrt{8}}{4}\right),$ • $\left(0,\,±\frac{\sqrt2}{2},\,-\frac{\sqrt{8}}{4}\right),$ • $\left(±\frac{\sqrt2}{2},\,0,\,-\frac{\sqrt{8}}{4}\right).$ 