Faster access than browser!Similarities between Icosahedral symmetry and Octahedral symmetry
Icosahedral symmetry and Octahedral symmetry have 28 things in common (in Unionpedia): Alternating group, Archimedean solid, Catalan solid, Conjugacy class, Coxeter notation, Cycle graph (algebra), Cyclic group, Dihedral group, Dihedral symmetry in three dimensions, Direct product of groups, Dual polyhedron, Harold Scott MacDonald Coxeter, Hermann–Mauguin notation, Index of a subgroup, List of finite spherical symmetry groups, List of small groups, Norman Johnson (mathematician), Orbifold notation, Platonic solid, Point groups in three dimensions, Point reflection, Schoenflies notation, Stereographic projection, Symmetric group, Symmetry group, Symmetry number, Tetrahedral symmetry, Translational symmetry.
Alternating group
In mathematics, an alternating group is the group of even permutations of a finite set.
Alternating group and Icosahedral symmetry · Alternating group and Octahedral symmetry ·
Archimedean solid
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.
Archimedean solid and Icosahedral symmetry · Archimedean solid and Octahedral symmetry ·
Catalan solid
In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid.
Catalan solid and Icosahedral symmetry · Catalan solid and Octahedral symmetry ·
Conjugacy class
In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.
Conjugacy class and Icosahedral symmetry · Conjugacy class and Octahedral symmetry ·
Coxeter notation
In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.
Coxeter notation and Icosahedral symmetry · Coxeter notation and Octahedral symmetry ·
Cycle graph (algebra)
In group theory, a sub-field of abstract algebra, a group cycle graph illustrates the various cycles of a group and is particularly useful in visualizing the structure of small finite groups.
Cycle graph (algebra) and Icosahedral symmetry · Cycle graph (algebra) and Octahedral symmetry ·
Cyclic group
In algebra, a cyclic group or monogenous group is a group that is generated by a single element.
Cyclic group and Icosahedral symmetry · Cyclic group and Octahedral symmetry ·
Dihedral group
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.
Dihedral group and Icosahedral symmetry · Dihedral group and Octahedral symmetry ·
Dihedral symmetry in three dimensions
In geometry, dihedral symmetry in three dimensions is one of three infinite sequences of point groups in three dimensions which have a symmetry group that as abstract group is a dihedral group Dihn (n ≥ 2).
Dihedral symmetry in three dimensions and Icosahedral symmetry · Dihedral symmetry in three dimensions and Octahedral symmetry ·
Direct product of groups
In group theory, the direct product is an operation that takes two groups and and constructs a new group, usually denoted.
Direct product of groups and Icosahedral symmetry · Direct product of groups and Octahedral symmetry ·
Dual polyhedron
In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.
Dual polyhedron and Icosahedral symmetry · Dual polyhedron and Octahedral symmetry ·
Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
Harold Scott MacDonald Coxeter and Icosahedral symmetry · Harold Scott MacDonald Coxeter and Octahedral symmetry ·
Hermann–Mauguin notation
In geometry, Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups.
Hermann–Mauguin notation and Icosahedral symmetry · Hermann–Mauguin notation and Octahedral symmetry ·
Index of a subgroup
In mathematics, specifically group theory, the index of a subgroup H in a group G is the "relative size" of H in G: equivalently, the number of "copies" (cosets) of H that fill up G. For example, if H has index 2 in G, then intuitively half of the elements of G lie in H. The index of H in G is usually denoted |G: H| or or (G:H).
Icosahedral symmetry and Index of a subgroup · Index of a subgroup and Octahedral symmetry ·
List of finite spherical symmetry groups
Finite spherical symmetry groups are also called point groups in three dimensions.
Icosahedral symmetry and List of finite spherical symmetry groups · List of finite spherical symmetry groups and Octahedral symmetry ·
List of small groups
The following list in mathematics contains the finite groups of small order up to group isomorphism.
Icosahedral symmetry and List of small groups · List of small groups and Octahedral symmetry ·
Norman Johnson (mathematician)
Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.
Icosahedral symmetry and Norman Johnson (mathematician) · Norman Johnson (mathematician) and Octahedral symmetry ·
Orbifold notation
In geometry, orbifold notation (or orbifold signature) is a system, invented by William Thurston and popularized by the mathematician John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature.
Icosahedral symmetry and Orbifold notation · Octahedral symmetry and Orbifold notation ·
Platonic solid
In three-dimensional space, a Platonic solid is a regular, convex polyhedron.
Icosahedral symmetry and Platonic solid · Octahedral symmetry and Platonic solid ·
Point groups in three dimensions
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.
Icosahedral symmetry and Point groups in three dimensions · Octahedral symmetry and Point groups in three dimensions ·
Point reflection
In geometry, a point reflection or inversion in a point (or inversion through a point, or central inversion) is a type of isometry of Euclidean space.
Icosahedral symmetry and Point reflection · Octahedral symmetry and Point reflection ·
Schoenflies notation
The Schoenflies (or Schönflies) notation, named after the German mathematician Arthur Moritz Schoenflies, is one of two conventions commonly used to describe point groups.
Icosahedral symmetry and Schoenflies notation · Octahedral symmetry and Schoenflies notation ·
Stereographic projection
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
Icosahedral symmetry and Stereographic projection · Octahedral symmetry and Stereographic projection ·
Symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.
Icosahedral symmetry and Symmetric group · Octahedral symmetry and Symmetric group ·
Symmetry group
In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.
Icosahedral symmetry and Symmetry group · Octahedral symmetry and Symmetry group ·
Symmetry number
The symmetry number or symmetry order of an object is the number of different but indistinguishable (or equivalent) arrangements (or views) of the object, i.e. the order of its symmetry group.
Icosahedral symmetry and Symmetry number · Octahedral symmetry and Symmetry number ·
Tetrahedral symmetry
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.
Icosahedral symmetry and Tetrahedral symmetry · Octahedral symmetry and Tetrahedral symmetry ·
Translational symmetry
In geometry, a translation "slides" a thing by a: Ta(p).
Icosahedral symmetry and Translational symmetry · Octahedral symmetry and Translational symmetry ·
The list above answers the following questions
- What Icosahedral symmetry and Octahedral symmetry have in common
- What are the similarities between Icosahedral symmetry and Octahedral symmetry
Icosahedral symmetry and Octahedral symmetry Comparison
Icosahedral symmetry has 96 relations, while Octahedral symmetry has 62. As they have in common 28, the Jaccard index is 17.72% = 28 / (96 + 62).
References
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