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The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron, the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid".
[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.
Square pyramids are added to the six square faces of the snub cube, and triangular pyramids are added to the eight triangular faces that do not share an edge with a square. The pyramid heights are adjusted to make them coplanar with the other 24 triangular faces of the snub cube. The result is the pentagonal icositetrahedron.
Triangular pyramid: Y 3 (A tetrahedron is a special pyramid) T = Y 3; O = aT (ambo tetrahedron) C = jT (join tetrahedron) I = sT (snub tetrahedron) D = gT (gyro tetrahedron) Triangular antiprism: A 3 (An octahedron is a special antiprism) O = A 3; C = dA 3; Square prism: P 4 (A cube is a special prism) C = P 4; Pentagonal antiprism: A 5. I = k ...
For example, a tetrakis hexahedron can be constructed by attaching the base of an equilateral square pyramid onto each face of a cube. [25] Attaching prisms or antiprisms to pyramids is known as elongation or gyroelongation, respectively. [26]
Net. In 4-dimensional geometry, the cubic pyramid is bounded by one cube on the base and 6 square pyramid cells which meet at the apex.Since a cube has a circumradius divided by edge length less than one, [1] the square pyramids can be made with regular faces by computing the appropriate height.
In geometry, the square gyrobicupola is one of the Johnson solids (J 29). Like the square orthobicupola ( J 28 ), it can be obtained by joining two square cupolae ( J 4 ) along their bases. The difference is that in this solid, the two halves are rotated 45 degrees with respect to one another.
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]