Elongated triangular pyramid
Elongated triangular pyramid (Johnson solid J7)
- What it is: A convex solid made by elongating a regular tetrahedron with a triangular prism attached to its base.
- Faces: 7 faces total — 4 equilateral triangles and 3 squares.
- Edges and vertices: 12 edges and 7 vertices.
- How it’s built: Start with a tetrahedron and attach a triangular prism to one base, replacing that base with three more triangles.
- Self-dual property: Topologically self-dual (faces and vertices correspond under duality).
- Symmetry: C3v symmetry (order 6); rotation group C3.
- Size with edge length a:
- Height h = (1 + sqrt(6)/3) a ≈ 1.816 a
- Surface area A = (3 + sqrt(3)) a^2 ≈ 4.732 a^2
- Volume V = (1/12)(sqrt(2) + 3 sqrt(3)) a^3 ≈ 0.551 a^3
- Note: It is one of the Johnson solids (the 7th in that list).
This page was last edited on 3 February 2026, at 15:50 (CET).