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Icosahedral symmetry and Triangle group

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Icosahedral symmetry and Triangle group

Icosahedral symmetry vs. Triangle group

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. In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle.

Similarities between Icosahedral symmetry and Triangle group

Icosahedral symmetry and Triangle group have 15 things in common (in Unionpedia): Belyi's theorem, Coxeter group, Dessin d'enfant, Dihedral group, Dodecahedron, Fundamental domain, Icosahedron, Icosian calculus, Index of a subgroup, Philosophical Magazine, Platonic solid, Point reflection, Presentation of a group, Symmetry group, William Rowan Hamilton.

Belyi's theorem

In mathematics, Belyi's theorem on algebraic curves states that any non-singular algebraic curve C, defined by algebraic number coefficients, represents a compact Riemann surface which is a ramified covering of the Riemann sphere, ramified at three points only.

Belyi's theorem and Icosahedral symmetry · Belyi's theorem and Triangle group · See more »

Coxeter group

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).

Coxeter group and Icosahedral symmetry · Coxeter group and Triangle group · See more »

Dessin d'enfant

In mathematics, a dessin d'enfant is a type of graph embedding used to study Riemann surfaces and to provide combinatorial invariants for the action of the absolute Galois group of the rational numbers.

Dessin d'enfant and Icosahedral symmetry · Dessin d'enfant and Triangle group · See more »

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 Triangle group · See more »

Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

Dodecahedron and Icosahedral symmetry · Dodecahedron and Triangle group · See more »

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.

Fundamental domain and Icosahedral symmetry · Fundamental domain and Triangle group · See more »

Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

Icosahedral symmetry and Icosahedron · Icosahedron and Triangle group · See more »

Icosian calculus

The icosian calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856.

Icosahedral symmetry and Icosian calculus · Icosian calculus and Triangle group · See more »

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 Triangle group · See more »

Philosophical Magazine

The Philosophical Magazine is one of the oldest scientific journals published in English.

Icosahedral symmetry and Philosophical Magazine · Philosophical Magazine and Triangle group · See more »

Platonic solid

In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

Icosahedral symmetry and Platonic solid · Platonic solid and Triangle group · See more »

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 · Point reflection and Triangle group · See more »

Presentation of a group

In mathematics, one method of defining a group is by a presentation.

Icosahedral symmetry and Presentation of a group · Presentation of a group and Triangle group · See more »

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 · Symmetry group and Triangle group · See more »

William Rowan Hamilton

Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician who made important contributions to classical mechanics, optics, and algebra.

Icosahedral symmetry and William Rowan Hamilton · Triangle group and William Rowan Hamilton · See more »

The list above answers the following questions

Icosahedral symmetry and Triangle group Comparison

Icosahedral symmetry has 96 relations, while Triangle group has 72. As they have in common 15, the Jaccard index is 8.93% = 15 / (96 + 72).

References

This article shows the relationship between Icosahedral symmetry and Triangle group. To access each article from which the information was extracted, please visit:

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