Elongated square bipyramid

Elongated square bipyramid
(3D model) (OFF file)
Rank	3
Type	CRF
Notation
Bowers style acronym	Esquidpy
Coxeter diagram	oxxo4oooo&#xt
Elements
Faces	8 triangles, 4 squares
Edges	4+8+8
Vertices	2+8
Vertex figures	2 squares, edge length 1
	8 kites, edge lengths 1 and √2
Measures (edge length 1)
Volume	${\frac {3+{\sqrt {2}}}{3}}\approx 1.47140$
Dihedral angles	3–4: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	3–3: $\arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }$
	4–4: 90°
Central density	1
Number of external pieces	12
Level of complexity	5
Related polytopes
Army	Esquidpy
Regiment	Esquidpy
Dual	Square bifrustum
Conjugate	None
Abstract & topological properties
Flag count	80
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	B2×A1, order 16
Convex	Yes
Nature	Tame

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

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

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)$,
• $\left(0,\,0,\,\pm {\frac {1+{\sqrt {2}}}{2}}\right)$.

Representations

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

• Klitzing, Richard. "esquidpy".
• Quickfur. "The Elongated Square Bipyramid".

• Wikipedia contributors. "Elongated square bipyramid".
• McCooey, David. "Elongated Square Dipyramid"