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In geometry, a square pyramid is a pyramid with a square base, having a total of five faces. If the apex of the pyramid is directly above the center of the square, it is a right square pyramid with four isosceles triangles; otherwise, it is an oblique square pyramid. When all of the pyramid's edges are equal in length, its triangles are all ...
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.
A pentagonal pyramid has six vertices, ten edges, and six faces. One of its faces is pentagon, a base of the pyramid; five others are triangles. [2] Five of the edges make up the pentagon by connecting its five vertices, and the other five edges are known as the lateral edges of the pyramid, meeting at the sixth vertex called the apex. [3]
[21] [22] A tetrahedron or triangular pyramid is an example that has four equilateral triangles, with all edges equal in length, and one of them is considered as the base. Because the faces are regular, it is an example of a Platonic solid and deltahedra, and it has tetrahedral symmetry. [23] [24] A pyramid with the base as circle is known as ...
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.
3D model of an elongated pentagonal bipyramid It has the same three-dimensional symmetry group as the pentagonal prism, the dihedral group D 5 h {\displaystyle D_{5\mathrm {h} }} of order 20. Its dihedral angle can be calculated by adding the angle of the pentagonal pyramid and pentagonal prism: [ 4 ]
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 a triangular bipyramid as a Johnson solid If the tetrahedra are regular, all edges of a triangular bipyramid are equal in length and form equilateral triangular faces . A polyhedron with only equilateral triangles as faces is called a deltahedron .