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.

Formulae

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

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

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

Dual polyhedron

The dual of the triangular cupola has 12 triangular faces:

Dual triangular cupola	Net of dual

External links

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