Elongated triangular pyramid

Elongated triangular pyramid
Type	Johnson J6 - J7 - J8
Faces	1+3 triangles 3 squares
Edges	12
Vertices	7
Vertex configuration	1(33) 3(3.42) 3(32.42)
Symmetry group	C3v, [3], (*33)
Rotation group	C3, [3]+, (33)
Dual polyhedron	self
Properties	convex
Net

In geometry, the elongated triangular pyramid is one of the Johnson solids (J₇). Norman Johnson discovered elongated triangular pyramids. As the name suggests, it can be constructed by elongating a tetrahedron by attaching a triangular prism to its base. Like any elongated pyramid, the resulting solid is topologically (but not geometrically) self-dual.

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

Formulae

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

$V=({\frac {1}{12}}({\sqrt {2}}+3{\sqrt {3}}))a^{3}\approx 0.550864...a^{3}$

$A=(3+{\sqrt {3}})a^{2}\approx 4.73205...a^{2}$

If the edges are not the same length, use the individual formulae for the tetrahedron and triangular prism separately, and add the results together.

Dual polyhedron

The dual of the elongated triangular pyramid has 7 faces: 4 triangular, and 3 trapezoidal.

Dual elongated triangular pyramid	Net of dual

External links

• Weisstein, Eric W. "Elongated triangular pyramid". MathWorld.
• Weisstein, Eric W. "Johnson solid". MathWorld.