Rectangular pyramid

Rectangular pyramid
(OFF file)
Rank	3
Notation
Bowers style acronym	Rectpy
Coxeter diagram	ox oy&#z
Elements
Faces	2+2 isosceles triangles, 1 rectangle
Edges	2+2+4
Vertices	1+4
Vertex figures	1 rectangle
	4 scalene triangles
Measures (edge lengths a, b [base], ℓ [lacing])
Circumradius	${\frac {l}{2{\sqrt {1-{\frac {a^{2}+b^{2}}{4l^{2}}}}}}}$
Volume	${\frac {1}{3}}ab{\sqrt {l^{2}-{\frac {a^{2}+b^{2}}{4}}}}$
Height	${\sqrt {l^{2}-{\frac {a^{2}+b^{2}}{4}}}}$
Central density	1
Related polytopes
Army	Rectpy
Regiment	Rectpy
Dual	Rhombic pyramid
Conjugate	Rectangular pyramid
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	K2×I, order 4
Convex	Yes
Nature	Tame

The rectangular pyramid, or rectpy, is a pyramid based on a rectangle. As such it has 1 rectangle base and 2 pairs of isosceles triangles as sides, with 3 types of edges.

In vertex figures

Rectangular pyramids occur as vertex figures in 4 prismatic uniform polychora, the cuboctahedral prism, icosidodecahedral prism, dodecadodecahedral prism, and great icosidodecahedral prism. Although a few other polychora have rectangle-based pyramids as vertex figures, these generally tend to have the symmetry of isosceles trapezoidal pyramids instead.