Square cupola

Square cupola
Type	Johnson J3 - J4 - J5
Faces	4 triangles 1+4 squares 1 octagon
Edges	20
Vertices	12
Vertex configuration	8(3.4.8) 4(3.43)
Symmetry group	C4v
Dual polyhedron	-
Properties	convex
Net

In geometry, the square cupola, sometimes called lesser dome, is one of the Johnson solids (J₄). It can be obtained as a slice of the rhombicuboctahedron. As in all cupolae, the base polygon has twice as many edges and vertices as the top; in this case the base polygon is an octagon.

Formulae

The following formulae for volume, surface area, and circumradius can be used if all faces are regular, with edge length a:

$V=(1+\frac{2\sqrt{2}}{3})a^3\approx1.94281...a^3$

$A=(7+2\sqrt{2}+\sqrt{3})a^2\approx11.5605...a^2$

$C=(\frac{1}{2}\sqrt{5+2\sqrt{2}})a\approx1.39897...a$

Dual polyhedron

The dual of the square cupola has 16 triangular faces:

Dual square cupolaamid	Net of dual

External links

• Eric W. Weisstein, Square cupola (Johnson solid) at MathWorld.