# Rectangular pyramid

Rectangular pyramid
Rank3
Notation
Bowers style acronymRectpy
Coxeter diagramox oy&#z
Elements
Faces2+2 isosceles triangles, 1 rectangle
Edges2+2+4
Vertices1+4
Vertex figures1 rectangle
4 scalene triangles
Measures (edge lengths a , b  [base], l  [lacing])
Circumradius${\displaystyle {\frac {l}{2{\sqrt {1-{\frac {a^{2}+b^{2}}{4l^{2}}}}}}}}$
Volume${\displaystyle {\frac {1}{3}}ab{\sqrt {l^{2}-{\frac {a^{2}+b^{2}}{4}}}}}$
Height${\displaystyle {\sqrt {l^{2}-{\frac {a^{2}+b^{2}}{4}}}}}$
Central density1
Related polytopes
ArmyRectpy
RegimentRectpy
DualRhombic pyramid
ConjugateRectangular pyramid
Abstract & topological properties
Flag count32
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryK2×I, order 4
Flag orbits8
ConvexYes
NatureTame

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.