Polyhedral group information

geometry, the polyhedral group is any of the symmetry groups of the Platonic solids. There are three polyhedral groups: The tetrahedral group of order 12...

polyhedral group (l,m,n). For instance, the preimage of the icosahedral group (2,3,5) is the binary icosahedral group, ⟨2,3,5⟩. The binary polyhedral...

Polyhedral cone Polyhedral cylinder Polyhedral convex function Polyhedral dice Polyhedral dual Polyhedral formula Polyhedral graph Polyhedral group Polyhedral...

of S U ( 2 ) {\displaystyle SU(2)} , the binary polyhedral groups; properly, binary polyhedral groups correspond to the simply laced affine Dynkin diagrams...

dicyclic group is a binary polyhedral group — it is one of the classes of subgroups of the Pin group Pin−(2), which is a subgroup of the Spin group Spin(3)...

Coxeter group, and like the polyhedral groups of 3D, it can be named by its related convex regular 4-polytope. Related pure rotational groups exist for...

special case of the binary polyhedral group ⟨ ℓ , m , n ⟩ {\displaystyle \langle \ell ,m,n\rangle } and related to the polyhedral group ( p , q , r ) {\displaystyle...

experiment. Binary polyhedral group Binary cyclic group, ⟨n⟩, order 2n Binary dihedral group, ⟨2,2,n⟩, order 4n Binary octahedral group, 2O = ⟨2,3,4⟩, order...

icosahedral group. binary polyhedral group binary cyclic group, ⟨n⟩, order 2n binary dihedral group, ⟨2,2,n⟩, order 4n binary tetrahedral group, 2T=⟨2,3...

polyhedral group corresponding to the cyclic group. In terms of binary polyhedral groups, the binary cyclic group is the preimage of the cyclic group...

SO(n).} Binary polyhedral group binary cyclic group, ⟨n⟩, index 2n binary dihedral group, ⟨2,2,n⟩, index 4n binary tetrahedral group, 2T=⟨2,3,3⟩, index...

studied – see point groups in three dimensions, polyhedral groups, and list of spherical symmetry groups. In 2 dimensions, the finite groups are either cyclic...

these shapes; however, these balls have rounded knobs rather than being polyhedral, the numbers of knobs frequently differed from the numbers of vertices...

2 or higher (n may be 1 as a special case). There are three types of polyhedral symmetry: tetrahedral symmetry, octahedral symmetry, and icosahedral symmetry...

2}j+{dt_{ad}-dt_{bc} \over 2}k\end{aligned}}} Anti-twister mechanism Binary polyhedral group Biquaternion Charts on SO(3) Clifford algebras Conversion between quaternions...

acro-n-gonal group (abstract group Zn); for n=1: no symmetry (trivial group) Achiral Cnh, [n+,2], (n*) of order 2n - prismatic symmetry or ortho-n-gonal group (abstract...

and hence there is a Galois connection between binary polyhedral groups and polyhedral groups, O(n) → PO(n) is a 2-to-1-cover, and hence has an analogous...

that is dual to an octahedron. The group of orientation-preserving symmetries is S4, the symmetric group or the group of permutations of four objects, since...

polychoric group is one of five symmetry groups of the 4-dimensional regular polytopes. There are also three polyhedral prismatic groups, and an infinite...

a rotation. The group of all (not necessarily orientation preserving) symmetries is isomorphic to the group S4, the symmetric group of permutations of...

Polyhedral space is a certain metric space. A (Euclidean) polyhedral space is a (usually finite) simplicial complex in which every simplex has a flat metric...

symplectic group. There are coincidences between symmetric/alternating groups and small groups of Lie type/polyhedral groups: S3 ≅ PSL2(2) ≅ dihedral group of...

"binary point groups"; most familiar is the 3-dimensional case, known as binary polyhedral groups. Concretely, every binary point group is either the...

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré...

infinite sequences of point groups in three dimensions which have a symmetry group that as an abstract group is a dihedral group Dihn (for n ≥ 2). There are...

upper surface, with each value being equally likely. Dice may also have polyhedral or irregular shapes, may have faces marked with numerals or symbols instead...

Nepovirus is a genus of viruses in the order Picornavirales, in the family Secoviridae, in the subfamily Comovirinae. Plants serve as natural hosts. There...

order greater than 2. These polyhedral groups are characterized by not having a C5 proper rotation axis. These polyhedral groups are characterized by having...

In geometry, a polyhedral compound is a figure that is composed of several polyhedra sharing a common centre. They are the three-dimensional analogs of...