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A regular tetrahedron, an example of a solid with full tetrahedral symmetry. A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.
The proper rotations, (order-3 rotation on a vertex and face, and order-2 on two edges) and reflection plane (through two faces and one edge) in the symmetry group of the regular tetrahedron The regular tetrahedron has 24 isometries, forming the symmetry group known as full tetrahedral symmetry T d {\displaystyle \mathrm {T} _{\mathrm {d} }} .
It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes. It contains the 75 nonprismatic uniform polyhedra , as well as 44 stellated forms of the convex regular and quasiregular polyhedra.
(rotating and 3D model) Type: Catalan: Conway notation: oC or deC Coxeter diagram: Face polygon: Kite with 3 equal acute angles & 1 obtuse angle Faces: 24, congruent: Edges: 24 short + 24 long = 48 Vertices: 8 (connecting 3 short edges) + 6 (connecting 4 long edges) + 12 (connecting 4 alternate short & long edges) = 26 Face configuration: V3.4. ...
A regular tetrahedron is invariant under twelve distinct rotations (if the identity transformation is included as a trivial rotation and reflections are excluded). These are illustrated here in the cycle graph format, along with the 180° edge (blue arrows) and 120° vertex (pink and orange arrows) rotations that permute the tetrahedron through the positions.
The compound of six tetrahedra with rotational freedom is a uniform polyhedron compound made of a symmetric arrangement of 6 tetrahedra, considered as antiprisms.It can be constructed by superimposing six tetrahedra within a cube, and then rotating them in pairs about the three axes that pass through the centres of two opposite cubic faces.
A uniform compound of four tetrahedra can be constructed by rotating tetrahedra along an axis of symmetry C 2 (that is the middle of an edge) in multiples of /.It has dihedral symmetry, D 8h, and the same vertex arrangement as the convex octagonal prism.
Each triangle can be mapped to another triangle of the same color by means of a 3D rotation alone. Triangles of different colors can be mapped to each other with a reflection or inversion in addition to rotations. Disdyakis triacontahedron hulls. The 62 vertices of a disdyakis triacontahedron are given by: [2]