Type: | Johnson |
Faces: | 4 triangles 3 squares |
Edges: | 12 |
Vertices: | 7 |
Dual: | self |
Properties: | convex |
Net: | Elongated Triangular Pyramid Net.svg |
In geometry, the elongated triangular pyramid is one of the Johnson solids . 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 elongated triangular pyramid is constructed from a triangular prism by attaching regular tetrahedron onto one of its bases, a process known as elongation. The tetrahedron covers an equilateral triangle, replacing it with three other equilateral triangles, so that the resulting polyhedron has four equilateral triangles and three squares as its faces. A convex polyhedron in which all of the faces are regular polygons is called the Johnson solid, and the elongated triangular pyramid is among them, enumerated as the seventh Johnson solid
J7
An elongated triangular pyramid with edge length
a
It has the three-dimensional symmetry group, the cyclic group
C3v
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.
The elongated triangular pyramid can form a tessellation of space with square pyramids and/or octahedra.[1]