Pentagonal pyramid

Pentagonal pyramid
Pentagonal pyramid
Type	Pyramid; Johnson; J1 – J2 – J3
Faces	5 triangles; 1 pentagon
Edges	10
Vertices	6
Vertex configuration
Symmetry group
Dihedral angle (degrees)	As a Johnson solid:; triangle-to-triangle: 138.19°; triangle-to-pentagon: 37.37°;
Dual polyhedron	self-dual
Properties	convex,; elementary (Johnson solid)
Net

In geometry, a pentagonal pyramid is a pyramid with a pentagon base and five triangular faces, having a total of six faces. It is categorized as a Johnson solid if all of the edges are equal in length, forming equilateral triangular faces and a regular pentagonal base.

Pentagonal pyramids occur as pieces and tools in the construction of many polyhedra. They also appear in the field of natural science, as in stereochemistry where the shape can be described as the pentagonal pyramidal molecular geometry, as well as the study of shell assembling in the underlying potential energy surfaces and disclination in fivelings and related shapes such as pyramidal copper and other metal nanowires.

Pentagonal pyramid

Type	Pyramid Johnson $J 1 - J 2 - J 3$
Faces	5 triangles 1 pentagon
Edges	10
Vertices	6
Vertex configuration	$5\times (3^{2}\times 5)+1\times 3^{5}$ ^[1]
Symmetry group	$C_{5\mathrm {v} }$
Dihedral angle (degrees)	As a Johnson solid: triangle-to-triangle: 138.19° triangle-to-pentagon: 37.37°
Dual polyhedron	self-dual
Properties	convex, elementary (Johnson solid)
Net