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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 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]
A triangular bipyramid is a known solution in the case of five electrons, placing vertices of a triangular bipyramid within a sphere. [18] This solution is aided by a mathematically rigorous computer. [19] A chemical compound's trigonal bipyramidal molecular geometry may be described as the atom cluster of a triangular bipyramid.
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.
Each layer represents one of the first five triangular numbers. A truncated triangular pyramid number [1] is found by removing some smaller tetrahedral number (or triangular pyramidal number) from each of the vertices of a bigger tetrahedral number. The number to be removed may be same or different from each of the vertices. [2]
The term often refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to a pyramid with any number of sides. [2] The numbers of points in the base and in layers parallel to the base are given by polygonal numbers of the given number of sides, while the numbers of points in each triangular side is ...
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.
In geometry, the elongated pyramids are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal prism. Along with the set of pyramids, these figures are topologically self-dual. There are three elongated pyramids that are Johnson solids: Elongated triangular pyramid (J 7), Elongated square pyramid (J 8), and