Square orthobicupola

Square orthobicupola
(3D model) (OFF file)
Rank	3
Type	CRF
Space	Spherical
Notation
Bowers style acronym	Squobcu
Coxeter diagram	xxx4oxo&#xt
Elements
Faces	8 triangles, 2+8 squares
Edges	4+4+8+16
Vertices	8+8
Vertex figures	8 isosceles trapezoids, edge lengths 1, √2, √2, √2
	8 kites, edge lengths 1 and √2
Measures (edge length 1)
Volume	$\frac{2(3+2\sqrt2)}{3} ≈ 3.88562$
Dihedral angles	3–4: $\arccos\left(-\frac{\sqrt6}{3}\right) ≈ 144.73561°$
	4–4 cupolaic: 135°
	3–3: $\arccos\left(-\frac13\right) ≈ 109.47122°$
	4–4 join: 90°
Central density	1
Related polytopes
Army	Squobcu
Regiment	Squobcu
Dual	Deltotrapezohedral hexadecahedron
Conjugate	Retrograde square orthobicupola
Abstract properties
Euler characteristic	2
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	B2×A1, order 16
Convex	Yes
Nature	Tame

The square orthobicupola is one of the 92 Johnson solids (J₂₈). It consists of 8 triangles and 2+8 squares. It can be constructed by attaching two square cupolas at their octagonal bases, such that the two square bases are in the same orientation.

If the cupolas are joined such that the bases are rotated 45°, the result is the square gyrobicupola.

Vertex coordinates

A square orthobicupola of edge length 1 has vertices given by the following coordinates:

• $\left(±\frac12,\,±\frac12,\,±\frac{\sqrt2}{2}\right),$
• $\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,0\right),$
• $\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,0\right).$

Related polyhedra

An octagonal prism can be inserted between the two halves of the square orthobicupola to produce the elongated square orthobicupola, better known as the uniform small rhombicuboctahedron.

External links

• Klitzing, Richard. "squobcu".

• Quickfur. "The Square Orthobicupola".

• Wikipedia Contributors. "Square orthobicupola".
• McCooey, David. "Square Orthobicupola"