Elongated triangular cupola

Elongated triangular cupola
Type Johnson
J17 - J18 - J19
Faces 1+3 triangles
3.3 squares
1 hexagon
Edges 27
Vertices 15
Vertex configuration 6(42.6)
3(3.4.3.4)
6(3.43)
Symmetry group C3v
Dual polyhedron -
Properties convex
Net

In geometry, the elongated triangular cupola is one of the Johnson solids (J18). As the name suggests, it can be constructed by elongating a triangular cupola (J3) by attaching a hexagonal prism to its base.

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

Contents

Formulae

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

V=(\frac{1}{6}(5\sqrt{2}%2B9\sqrt{3}))a^3\approx3.77659...a^3

A=(9%2B\frac{5\sqrt{3}}{2})a^2\approx13.3301...a^2

Dual polyhedron

The dual of the elongated triangular cupola has 15 faces: 6 isoceles triangles, 3 rhombi, 6 quadrilaterals.

Dual elongated triangular cupola Net of dual

References

  1. ^ Stephen Wolfram, "Elongated triangular cupola" from Wolfram Alpha. Retrieved July 22, 2010.

External links