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.

Contents

Formulae

The following formulae for volume, surface area, and circumradius can be used if all faces are regular, with edge length a:[1]

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

A=(7%2B2\sqrt{2}%2B\sqrt{3})a^2\approx11.5605...a^2

C=(\frac{1}{2}\sqrt{5%2B2\sqrt{2}})a\approx1.39897...a

Dual polyhedron

The dual of the square cupola has 16 triangular faces:

Dual square cupolaamid Net of dual

References

  1. ^ Stephen Wolfram, "Square cupola" from Wolfram Alpha. Retrieved July 20, 2010.

External links