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The two dodecahedra project onto the decagonal faces of the envelope. The dodecahedron-first orthographic projection of the dodecahedral prism into 3D space has a dodecahedral envelope. The two dodecahedral cells project onto the entire volume of this envelope, while the 12 pentagonal prism cells project onto its 12 pentagonal faces.
Each face of a central dodecahedron is attached with two pentagonal pyramids, creating 24 pentagonal pyramidal cells, 72 isosceles triangular faces, 70 edges, and 22 vertices. A dodecahedral bipyramid can be seen as two dodecahedral pyramids augmented together at their base. It is the dual of a icosahedral prism.
A normal triangle is a 2-dimensional hyperpyramid, the triangular pyramid is a 3-dimensional hyperpyramid and the pentachoron or tetrahedral pyramid is a 4-dimensional hyperpyramid with a tetrahedron as base. The n-dimensional volume of a n-dimensional hyperpyramid can be computed as follows: = Here V n denotes the n-dimensional volume of the ...
A bipyramid is a polyhedron constructed by fusing two pyramids which share the same polygonal base; [1] a pyramid is in turn constructed by connecting each vertex of its base to a single new vertex (the apex) not lying in the plane of the base, for an n-gonal base forming n triangular faces in addition to the base face.
The base regularity of a pyramid's base may be classified based on the type of polygon: one example is the star pyramid in which its base is the regular star polygon. [28] The truncated pyramid is a pyramid cut off by a plane; if the truncation plane is parallel to the base of a pyramid, it is called a frustum.
A triangular bipyramid is a hexahedron with six triangular faces constructed by attaching two tetrahedra face-to-face. The same shape is also known as a triangular dipyramid [1] [2] or trigonal bipyramid. [3] If these tetrahedra are regular, all faces of a triangular bipyramid are equilateral.
In geometry, the snub disphenoid is a convex polyhedron with 12 equilateral triangles as its faces. It is an example of deltahedron and Johnson solid. It can be constructed in different approaches. This shape is also called Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron.
In the case of a triangular prism, its base is a triangle, so its volume can be calculated by multiplying the area of a triangle and the length of the prism: , where b is the length of one side of the triangle, h is the length of an altitude drawn to that side, and l is the distance between the triangular faces. [9]