Type Johnson
J6 - J7 - J8 Vertices 7 Symmetry group C3v, [3], (*33) | Edges 12 Vertex configuration 1(3)
3(3.4)
3(3.4) | |
 | ||
Faces 1+3 triangles
3 squares | ||
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.
Contents
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.
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:
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
Topologically, the elongated triangular pyramid is its own dual. Geometrically, the dual has seven irregular faces: one equilateral triangle, three isosceles triangles and three isosceles trapezoids.
Related polyhedra and honeycombs
The elongated triangular pyramid can form a tessellation of space with square pyramids and/or octahedra.