Faster access than browser!Similarities between Coxeter–Dynkin diagram and Uniform polytope
Coxeter–Dynkin diagram and Uniform polytope have 32 things in common (in Unionpedia): Alternation (geometry), Convex uniform honeycomb, Coxeter notation, E6 (mathematics), E7 (mathematics), E8 (mathematics), Edge (geometry), Face (geometry), Facet (geometry), Fundamental domain, Harold Scott MacDonald Coxeter, Hyperplane, Norman Johnson (mathematician), Octahedral symmetry, Polygon, Polytope, Prism (geometry), Pyramid (geometry), Rational number, Regular polygon, Regular polytope, Schläfli symbol, Simple Lie group, Simplex, Snub (geometry), Square, Tetrahedron, Uniform 4-polytope, Uniform polyhedron, Uniform tiling, ..., Wythoff construction, Wythoff symbol. Expand index (2 more) »
Alternation (geometry)
In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.
Alternation (geometry) and Coxeter–Dynkin diagram · Alternation (geometry) and Uniform polytope ·
Convex uniform honeycomb
In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.
Convex uniform honeycomb and Coxeter–Dynkin diagram · Convex uniform honeycomb and Uniform polytope ·
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 Coxeter–Dynkin diagram · Coxeter notation and Uniform polytope ·
E6 (mathematics)
In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras \mathfrak_6, all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6.
Coxeter–Dynkin diagram and E6 (mathematics) · E6 (mathematics) and Uniform polytope ·
E7 (mathematics)
In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7.
Coxeter–Dynkin diagram and E7 (mathematics) · E7 (mathematics) and Uniform polytope ·
E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8.
Coxeter–Dynkin diagram and E8 (mathematics) · E8 (mathematics) and Uniform polytope ·
Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
Coxeter–Dynkin diagram and Edge (geometry) · Edge (geometry) and Uniform polytope ·
Face (geometry)
In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.
Coxeter–Dynkin diagram and Face (geometry) · Face (geometry) and Uniform polytope ·
Facet (geometry)
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
Coxeter–Dynkin diagram and Facet (geometry) · Facet (geometry) and Uniform polytope ·
Fundamental domain
Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action.
Coxeter–Dynkin diagram and Fundamental domain · Fundamental domain and Uniform polytope ·
Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
Coxeter–Dynkin diagram and Harold Scott MacDonald Coxeter · Harold Scott MacDonald Coxeter and Uniform polytope ·
Hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
Coxeter–Dynkin diagram and Hyperplane · Hyperplane and Uniform polytope ·
Norman Johnson (mathematician)
Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.
Coxeter–Dynkin diagram and Norman Johnson (mathematician) · Norman Johnson (mathematician) and Uniform polytope ·
Octahedral symmetry
A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and a symmetry order of 48 including transformations that combine a reflection and a rotation.
Coxeter–Dynkin diagram and Octahedral symmetry · Octahedral symmetry and Uniform polytope ·
Polygon
In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
Coxeter–Dynkin diagram and Polygon · Polygon and Uniform polytope ·
Polytope
In elementary geometry, a polytope is a geometric object with "flat" sides.
Coxeter–Dynkin diagram and Polytope · Polytope and Uniform polytope ·
Prism (geometry)
In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.
Coxeter–Dynkin diagram and Prism (geometry) · Prism (geometry) and Uniform polytope ·
Pyramid (geometry)
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.
Coxeter–Dynkin diagram and Pyramid (geometry) · Pyramid (geometry) and Uniform polytope ·
Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
Coxeter–Dynkin diagram and Rational number · Rational number and Uniform polytope ·
Regular polygon
In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
Coxeter–Dynkin diagram and Regular polygon · Regular polygon and Uniform polytope ·
Regular polytope
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.
Coxeter–Dynkin diagram and Regular polytope · Regular polytope and Uniform polytope ·
Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
Coxeter–Dynkin diagram and Schläfli symbol · Schläfli symbol and Uniform polytope ·
Simple Lie group
In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.
Coxeter–Dynkin diagram and Simple Lie group · Simple Lie group and Uniform polytope ·
Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
Coxeter–Dynkin diagram and Simplex · Simplex and Uniform polytope ·
Snub (geometry)
In geometry, a snub is an operation applied to a polyhedron.
Coxeter–Dynkin diagram and Snub (geometry) · Snub (geometry) and Uniform polytope ·
Square
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.
Coxeter–Dynkin diagram and Square · Square and Uniform polytope ·
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–Dynkin diagram and Tetrahedron · Tetrahedron and Uniform polytope ·
Uniform 4-polytope
In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.
Coxeter–Dynkin diagram and Uniform 4-polytope · Uniform 4-polytope and Uniform polytope ·
Uniform polyhedron
A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).
Coxeter–Dynkin diagram and Uniform polyhedron · Uniform polyhedron and Uniform polytope ·
Uniform tiling
In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive.
Coxeter–Dynkin diagram and Uniform tiling · Uniform polytope and Uniform tiling ·
Wythoff construction
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.
Coxeter–Dynkin diagram and Wythoff construction · Uniform polytope and Wythoff construction ·
Wythoff symbol
In geometry, the Wythoff symbol represents a Wythoff construction of a uniform polyhedron or plane tiling, from a Schwarz triangle.
Coxeter–Dynkin diagram and Wythoff symbol · Uniform polytope and Wythoff symbol ·
The list above answers the following questions
- What Coxeter–Dynkin diagram and Uniform polytope have in common
- What are the similarities between Coxeter–Dynkin diagram and Uniform polytope
Coxeter–Dynkin diagram and Uniform polytope Comparison
Coxeter–Dynkin diagram has 117 relations, while Uniform polytope has 150. As they have in common 32, the Jaccard index is 11.99% = 32 / (117 + 150).
References
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