Triangular cupola

Triangular cupola
Type Johnson
J2 - J3 - J4
Faces 1+3 triangles
3 squares
1 hexagon
Edges 15
Vertices 9
Vertex configuration 6(3.4.6)
3(3.4.3.4)
Symmetry group C3v
Dual polyhedron -
Properties convex
Net

In geometry, the triangular cupola is one of the Johnson solids (J3). It can be seen as half a cuboctahedron.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

Contents

Formulae

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

V=(\frac{5}{3\sqrt{2}})a^3\approx1.17851...a^3

A=(3%2B\frac{5\sqrt{3}}{2})a^2\approx7.33013...a^2

Dual polyhedron

The dual of the triangular cupola has 12 triangular faces:

Dual triangular cupola Net of dual

References

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

External links