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3D model of an equilateral square pyramid. If all triangular edges are of equal length, the four triangles are equilateral, and the pyramid's faces are all regular polygons, it is an equilateral square pyramid. [13]
3D model of a pentagonal pyramid When all edges are equal in length, the five triangular faces are equilateral and the base is a regular pentagon. Because this pyramid remains convex and all of its faces are regular polygons , it is classified as the second Johnson solid J 2 {\displaystyle J_{2}} . [ 7 ]
A space-filling tetrahedral disphenoid inside a cube. Two edges have dihedral angles of 90°, and four edges have dihedral angles of 60°. A disphenoid is a tetrahedron with four congruent triangles as faces; the triangles necessarily have all angles acute. The regular tetrahedron is a special case of a disphenoid.
A hexagonal pyramid has seven vertices, twelve edges, and seven faces. One of its faces is hexagon, a base of the pyramid; six others are triangles. Six of the edges make up the pentagon by connecting its six vertices, and the other six edges are known as the lateral edges of the pyramid, meeting at the seventh vertex called the apex.
[19] [20] Examples are square pyramid and pentagonal pyramid, a four- and five-triangular faces pyramid with a square and pentagon base, respectively; they are classified as the first and second Johnson solid if their regular faces and edges that are equal in length, and their symmetries are C 4v of order 8 and C 5v of order 10, respectively.
3D model of a pentagonal bipyramid as a Johnson solid If the pyramids are regular, all edges of the triangular bipyramid are equal in length, making up the faces equilateral triangles . A polyhedron with only equilateral triangles as faces is called a deltahedron . [ 9 ]
3D model of an elongated pentagonal pyramid In geometry , the elongated pentagonal pyramid is one of the Johnson solids ( J 9 ). As the name suggests, it can be constructed by elongating a pentagonal pyramid ( J 2 ) by attaching a pentagonal prism to its base.
A dodecagonal pyramid is a pyramid with a dodecagonal base. It is a type of tridecahedron, which has 13 faces , 24 edges , and 13 vertices , and its dual polyhedron is itself. [ 5 ] A regular dodecagonal pyramid is a dodecagonal pyramid whose base is a regular dodecagon.