Elongated pentagonal pyramid | |
---|---|
![]() | |
Type | Johnson J8 – J9 – J10 |
Faces | 5 triangles 5 squares 1 pentagon |
Edges | 20 |
Vertices | 11 |
Vertex configuration | 5(42.5) 5(32.42) 1(35) |
Symmetry group | C5v, [5], (*55) |
Rotation group | C5, [5]+, (55) |
Dual polyhedron | self-dual [1] |
Properties | convex |
Net | |
![]() |
The elongated pentagonal pyramid is a polyhedron constructed by attaching one pentagonal pyramid onto one of the pentagonal prism's bases, a process known as elongation. It is an example of composite polyhedron. [2] [3] This construction involves the removal of one pentagonal face and replacing it with the pyramid. The resulting polyhedron has five equilateral triangles, five squares, and one pentagon as its faces. [4] It remains convex, with the faces are all regular polygons, so the elongated pentagonal pyramid is Johnson solid, enumerated as the sixteenth Johnson solid . [5]
For edge length , an elongated pentagonal pyramid has a surface area by summing the area of all faces, and volume by totaling the volume of a pentagonal pyramid's Johnson solid and regular pentagonal prism: [4]
The elongated pentagonal pyramid has a dihedral between its adjacent faces: [6]