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 group of all (not necessarily orientation preserving) symmetries is isomorphic to the group S4, the symmetric group of permutations of four objects, since there is exactly one such symmetry for each permutation of the vertices of the tetrahedron. The set of orientation-preserving symmetries forms a group referred to as the alternating subgroup A4 of S4.
and 26 Related for: Tetrahedral symmetry information
symmetries forms a group referred to as the alternating subgroup A4 of S4. Chiral and full (or achiral tetrahedralsymmetry and pyritohedral symmetry)...
isometries, forming the symmetry group known as full tetrahedralsymmetry T d {\displaystyle \mathrm {T} _{\mathrm {d} }} . This symmetry group is isomorphic...
common crystal form in pyrite, has pyritohedral symmetry, while the tetartoid has tetrahedralsymmetry. The rhombic dodecahedron can be seen as a limiting...
triangular fundamental domains: dihedral, cyclic, tetrahedral, octahedral, and icosahedral symmetry. This article lists the groups by Schoenflies notation...
order 24, is chiral octahedral symmetry or rotational octahedral symmetry . This group is like chiral tetrahedralsymmetry T, but the C2 axes are now C4...
{\displaystyle \mathrm {O} _{\mathrm {h} }} , and the same symmetry as the regular tetrahedron, tetrahedralsymmetry T d {\displaystyle \mathrm {T} _{\mathrm {d} }}...
octahedral symmetry, but they can be colored to have only tetrahedralsymmetry. Rectification and snub also exist with tetrahedralsymmetry, but they are...
perfectly symmetrical tetrahedral molecules belong to point group Td, but most tetrahedral molecules have lower symmetry. Tetrahedral molecules can be chiral...
technique can be applied to construct polyhedra with tetrahedralsymmetry and octahedral symmetry. These polyhedra will have triangles or squares rather...
that has at most tetrahedralsymmetry. (All Platonic solids have at least tetrahedralsymmetry, as tetrahedralsymmetry is a symmetry operation of (i.e...
(3*2), [3+,4], with order 24. Tetrahedralsymmetry has the symbol (332), [3,3]+, with order 12. These lower symmetries allow geometric distortions from...
remain isosceles. It has chiral tetrahedralsymmetry, and so its geometry can be constructed from pyritohedral symmetry of the pseudoicosahedron with 4...
should be obvious from their names. Tetrahedralsymmetry is not present in Callimitra agnesae. Spherical symmetry is characterised by the ability to draw...
any of the symmetry groups of the Platonic solids. There are three polyhedral groups: The tetrahedral group of order 12, rotational symmetry group of the...
if these cupolas are appropriately chosen, then this toroid has tetrahedralsymmetry. There is only one uniform coloring of the faces of this polyhedron...
is the simplest alkane with a quaternary carbon, and has achiral tetrahedralsymmetry. It is one of the three structural isomers with the molecular formula...
eleven arrangements of nets. The uniform tetrahemihexahedron is a tetrahedralsymmetry faceting of the regular octahedron, sharing edge and vertex arrangement...
approximately 1.07 times as long as the other edges. This polyhedron has tetrahedralsymmetry. Topologically, as a near-miss Johnson solid, the four triangles...
4-dimensional symmetry groups. Rank 4 Coxeter groups allow a set of 4 mirrors to span 4-space, and divides the 3-sphere into tetrahedral fundamental domains...
2010-02-17. Retrieved 2009-09-28. Weisstein, Eric W. "Symmetry Group". MathWorld. Weisstein, Eric W. "Tetrahedral Group". MathWorld. Overview of the 32 crystallographic...
two uniform colorings, with tetrahedralsymmetry and octahedral symmetry, and two 2-uniform coloring with dihedral symmetry as a truncated triangular antiprism...
(having the hexagonal faces in common). By Wythoff construction it has tetrahedralsymmetry (Td), like the rhombitetratetrahedron construction for the cuboctahedron...
notation these groups are tetrahedralsymmetry [3,3], octahedral symmetry [4,3], icosahedral symmetry [5,3], and dihedral symmetry [p,2]. The number of mirrors...
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