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The regular complex polytope 4 {4} 2, , in has a real representation as a tesseract or 4-4 duoprism in 4-dimensional space. 4 {4} 2 has 16 vertices, and 8 4-edges. Its symmetry is 4 [4] 2, order 32. It also has a lower symmetry construction, , or 4 {}× 4 {}, with symmetry 4 [2] 4, order 16. This is the symmetry if the red and blue 4-edges are ...
A cube is a special case of rectangular cuboid in which the edges are equal in length. [1] Like other cuboids, every face of a cube has four vertices, each of which connects with three congruent lines. These edges form square faces, making the dihedral angle of a cube between every two adjacent squares being the interior angle of a square, 90 ...
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 .
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]
These two tetrahedra's vertices combined are the vertices of a cube, demonstrating that the regular tetrahedron is the 3-demicube, a polyhedron that is by alternating a cube. This form has Coxeter diagram and Schläfli symbol h { 4 , 3 } {\displaystyle \mathrm {h} \{4,3\}} .
The eight vertices of a cube have the coordinates (±1, ±1, ±1). ... called a triangular gyrobianticupola. It has D 3d symmetry, order 12. It has 2 sets of 3 ...
A twisted prism cannot be dissected into tetrahedra without adding new vertices. The simplest twisted prism has triangle bases and is called a Schönhardt polyhedron. An n-gonal twisted prism is topologically identical to the n-gonal uniform antiprism, but has half the symmetry group: D n, [n,2] +, order 2n. It can be seen as a nonconvex ...
All hypercubes have lower symmetry forms constructed as prisms. The 5-cube has 7 prismatic forms from the lowest 5-orthotope, { } 5, and upwards as orthogonal edges are constrained to be of equal length. The vertices in a prism are equal to the product of the vertices in the elements.