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In geometry, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary convex polyhedra. [1]
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.
A right pyramid is a pyramid whose base is circumscribed about a circle and the altitude of the pyramid meets the base at the circle's center; otherwise, it is oblique. [12] This pyramid may be classified based on the regularity of its bases. A pyramid with a regular polygon as the base is called a regular pyramid. [13]
In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.
The elongated triangular bipyramid is constructed from a triangular prism by attaching two tetrahedrons onto its bases, a process known as the elongation. [1] These tetrahedrons cover the triangular faces so that the resulting polyhedron has nine faces (six of them are equilateral triangles and three of them are squares), fifteen edges, and eight vertices. [2]
The edges and vertices of the triaugmented triangular prism form a maximal planar graph with 9 vertices and 21 edges, called the Fritsch graph. It was used by Rudolf and Gerda Fritsch to show that Alfred Kempe 's attempted proof of the four color theorem was incorrect.