Similarities between Coxeter group and Regular icosahedron
Coxeter group and Regular icosahedron have 19 things in common (in Unionpedia): Abelian group, Coxeter element, Coxeter–Dynkin diagram, Dodecahedron, Dual polyhedron, Eigenvalues and eigenvectors, Hyperbolic space, Icosahedral symmetry, Icosahedron, Normal subgroup, Octahedron, Regular polyhedron, Symmetric group, Symmetric matrix, Symmetry group, Tetrahedron, 6-cube, 6-demicube, 6-orthoplex.
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
Abelian group and Coxeter group · Abelian group and Regular icosahedron ·
Coxeter element
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
Coxeter element and Coxeter group · Coxeter element and Regular icosahedron ·
Coxeter–Dynkin diagram
In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).
Coxeter group and Coxeter–Dynkin diagram · Coxeter–Dynkin diagram and Regular icosahedron ·
Dodecahedron
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.
Coxeter group and Dodecahedron · Dodecahedron and Regular icosahedron ·
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.
Coxeter group and Dual polyhedron · Dual polyhedron and Regular icosahedron ·
Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
Coxeter group and Eigenvalues and eigenvectors · Eigenvalues and eigenvectors and Regular icosahedron ·
Hyperbolic space
In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.
Coxeter group and Hyperbolic space · Hyperbolic space and Regular icosahedron ·
Icosahedral symmetry
A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.
Coxeter group and Icosahedral symmetry · Icosahedral symmetry and Regular icosahedron ·
Icosahedron
In geometry, an icosahedron is a polyhedron with 20 faces.
Coxeter group and Icosahedron · Icosahedron and Regular icosahedron ·
Normal subgroup
In abstract algebra, a normal subgroup is a subgroup which is invariant under conjugation by members of the group of which it is a part.
Coxeter group and Normal subgroup · Normal subgroup and Regular icosahedron ·
Octahedron
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
Coxeter group and Octahedron · Octahedron and Regular icosahedron ·
Regular polyhedron
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.
Coxeter group and Regular polyhedron · Regular icosahedron and Regular polyhedron ·
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.
Coxeter group and Symmetric group · Regular icosahedron and Symmetric group ·
Symmetric matrix
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.
Coxeter group and Symmetric matrix · Regular icosahedron and Symmetric matrix ·
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.
Coxeter group and Symmetry group · Regular icosahedron and Symmetry group ·
Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
Coxeter group and Tetrahedron · Regular icosahedron and Tetrahedron ·
6-cube
In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.
6-cube and Coxeter group · 6-cube and Regular icosahedron ·
6-demicube
In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.
6-demicube and Coxeter group · 6-demicube and Regular icosahedron ·
6-orthoplex
In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5-cell 4-faces, and 64 5-faces.
6-orthoplex and Coxeter group · 6-orthoplex and Regular icosahedron ·
The list above answers the following questions
- What Coxeter group and Regular icosahedron have in common
- What are the similarities between Coxeter group and Regular icosahedron
Coxeter group and Regular icosahedron Comparison
Coxeter group has 141 relations, while Regular icosahedron has 163. As they have in common 19, the Jaccard index is 6.25% = 19 / (141 + 163).
References
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