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). 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.

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.

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

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

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