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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".
[17] [18] A tetrahedron or triangular pyramid is an example that has four equilateral triangles, with all edges equal in length, and one of them is considered as the base. Because the faces are regular, it is an example of a Platonic solid and deltahedra, and it has tetrahedral symmetry. [19] [20] A pyramid with the base as circle is known as ...
Basic three-dimensional cell shapes. The basic 3-dimensional element are the tetrahedron, quadrilateral pyramid, triangular prism, and hexahedron. They all have triangular and quadrilateral faces. Extruded 2-dimensional models may be represented entirely by the prisms and hexahedra as extruded triangles and quadrilaterals.
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.
Alternatively, if you expand each of five cubes by moving the faces away from the origin the right amount and rotating each of the five 72° around so they are equidistant from each other, without changing the orientation or size of the faces, and patch the pentagonal and triangular holes in the result, you get a rhombicosidodecahedron ...
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 ...
The graph perspective allows one to apply graph terminology and properties to polyhedra. For example, the tetrahedron and Császár polyhedron are the only known polyhedra whose skeletons are complete graphs (K 4), and various symmetry restrictions on polyhedra give rise to skeletons that are symmetric graphs.
A pyramid with side length 5 contains 35 spheres. Each layer represents one of the first five triangular numbers. A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron.