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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 ...
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 ]
[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 ...
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 ]
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 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 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.
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 .