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A triangular prism has 6 vertices, 9 edges, and 5 faces. Every prism has 2 congruent faces known as its bases, and the bases of a triangular prism are triangles. The triangle has 3 vertices, each of which pairs with another triangle's vertex, making up another 3 edges. These edges form 3 parallelograms as other faces. [2]
The above embedding divides the cube into five tetrahedra, one of which is regular. In fact, five is the minimum number of tetrahedra required to compose a cube. To see this, starting from a base tetrahedron with 4 vertices, each added tetrahedra adds at most 1 new vertex, so at least 4 more must be added to make a cube, which has 8 vertices.
The smallest polyhedron is the tetrahedron with 4 triangular faces, 6 edges, and 4 vertices. Named polyhedra primarily come from the families of platonic solids , Archimedean solids , Catalan solids , and Johnson solids , as well as dihedral symmetry families including the pyramids , bipyramids , prisms , antiprisms , and trapezohedrons .
Its (n + 1)-polytope prism will have 2F i + F i−1 i-face elements. (With F −1 = 0, F n = 1.) By dimension: Take a polygon with n vertices, n edges. Its prism has 2n vertices, 3n edges, and 2 + n faces. Take a polyhedron with V vertices, E edges, and F faces. Its prism has 2V vertices, 2E + V edges, 2F + E faces, and 2 + F cells.
Rarely, a right pyramid is defined to be a pyramid whose base is circumscribed about a circle and the altitude of the pyramid meets the base at the circle's center. [17] For the pyramid with an n-sided regular base, it has n + 1 vertices, n + 1 faces, and 2n edges. [18]
A quadrilaterally-based pyramid has 5 vertices, 8 edges, bounded by 4 triangular and 1 quadrilateral face. These are effectively used as transition elements between square and triangular faced elements and other in hybrid meshes and grids.
If the pyramid's apex lies on a line erected perpendicularly from the center of the square, it is called a right square pyramid, and the four triangular faces are isosceles triangles. Otherwise, the pyramid has two or more non-isosceles triangular faces and is called an oblique square pyramid. [4]
It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. ... 4: 6: 4: 4{3} Triangular prism: 3.4.4: