Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Install
Faster access than browser!
 

Icosahedral symmetry and Regular icosahedron

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

Difference between Icosahedral symmetry and Regular icosahedron

Icosahedral symmetry vs. Regular icosahedron

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 geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices.

Similarities between Icosahedral symmetry and Regular icosahedron

Icosahedral symmetry and Regular icosahedron have 32 things in common (in Unionpedia): Alternating group, Antiprism, Capsid, Chirality (mathematics), Compound of five octahedra, Coxeter group, Coxeter–Dynkin diagram, Dihedral symmetry in three dimensions, Dodecahedron, Dual polyhedron, Felix Klein, Great dodecahedron, Great icosahedron, Icosahedron, Isomorphism, Kepler–Poinsot polyhedron, List of finite spherical symmetry groups, Normal subgroup, Orbifold notation, Platonic solid, Quintic function, Radiolaria, Regular dodecahedron, Rhombic triacontahedron, Small stellated dodecahedron, Snub dodecahedron, Stereographic projection, Symmetric group, Symmetry group, Tetrahedral symmetry, ..., Truncated icosahedron, Virus. Expand index (2 more) »

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 Regular icosahedron · See more »

Antiprism

In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles.

Antiprism and Icosahedral symmetry · Antiprism and Regular icosahedron · See more »

Capsid

A capsid is the protein shell of a virus.

Capsid and Icosahedral symmetry · Capsid and Regular icosahedron · See more »

Chirality (mathematics)

In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone.

Chirality (mathematics) and Icosahedral symmetry · Chirality (mathematics) and Regular icosahedron · See more »

Compound of five octahedra

The compound of five octahedra is one of the five regular polyhedron compounds.

Compound of five octahedra and Icosahedral symmetry · Compound of five octahedra and Regular icosahedron · 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 Regular icosahedron · See more »

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–Dynkin diagram and Icosahedral symmetry · Coxeter–Dynkin diagram and Regular icosahedron · See more »

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 Regular icosahedron · 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 Regular icosahedron · See more »

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 Regular icosahedron · See more »

Felix Klein

Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory.

Felix Klein and Icosahedral symmetry · Felix Klein and Regular icosahedron · See more »

Great dodecahedron

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of.

Great dodecahedron and Icosahedral symmetry · Great dodecahedron and Regular icosahedron · See more »

Great icosahedron

In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol and Coxeter-Dynkin diagram of.

Great icosahedron and Icosahedral symmetry · Great icosahedron and Regular icosahedron · See more »

Icosahedron

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

Icosahedral symmetry and Icosahedron · Icosahedron and Regular icosahedron · See more »

Isomorphism

In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.

Icosahedral symmetry and Isomorphism · Isomorphism and Regular icosahedron · See more »

Kepler–Poinsot polyhedron

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.

Icosahedral symmetry and Kepler–Poinsot polyhedron · Kepler–Poinsot polyhedron and Regular icosahedron · See more »

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 Regular icosahedron · See more »

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.

Icosahedral symmetry and Normal subgroup · Normal subgroup and Regular icosahedron · See more »

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 · Orbifold notation and Regular icosahedron · See more »

Platonic solid

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

Icosahedral symmetry and Platonic solid · Platonic solid and Regular icosahedron · See more »

Quintic function

In algebra, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.

Icosahedral symmetry and Quintic function · Quintic function and Regular icosahedron · See more »

Radiolaria

The Radiolaria, also called Radiozoa, are protozoa of diameter 0.1–0.2 mm that produce intricate mineral skeletons, typically with a central capsule dividing the cell into the inner and outer portions of endoplasm and ectoplasm.The elaborate mineral skeleton is usually made of silica.

Icosahedral symmetry and Radiolaria · Radiolaria and Regular icosahedron · See more »

Regular dodecahedron

A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of twelve regular pentagonal faces, three meeting at each vertex.

Icosahedral symmetry and Regular dodecahedron · Regular dodecahedron and Regular icosahedron · See more »

Rhombic triacontahedron

In geometry, the rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces.

Icosahedral symmetry and Rhombic triacontahedron · Regular icosahedron and Rhombic triacontahedron · See more »

Small stellated dodecahedron

In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.

Icosahedral symmetry and Small stellated dodecahedron · Regular icosahedron and Small stellated dodecahedron · See more »

Snub dodecahedron

In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.

Icosahedral symmetry and Snub dodecahedron · Regular icosahedron and Snub dodecahedron · See more »

Stereographic projection

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.

Icosahedral symmetry and Stereographic projection · Regular icosahedron and Stereographic projection · See more »

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 · Regular icosahedron and Symmetric 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 · Regular icosahedron and Symmetry group · See more »

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 · Regular icosahedron and Tetrahedral symmetry · See more »

Truncated icosahedron

In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose faces are two or more types of regular polygons.

Icosahedral symmetry and Truncated icosahedron · Regular icosahedron and Truncated icosahedron · See more »

Virus

A virus is a small infectious agent that replicates only inside the living cells of other organisms.

Icosahedral symmetry and Virus · Regular icosahedron and Virus · See more »

The list above answers the following questions

Icosahedral symmetry and Regular icosahedron Comparison

Icosahedral symmetry has 96 relations, while Regular icosahedron has 163. As they have in common 32, the Jaccard index is 12.36% = 32 / (96 + 163).

References

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

Hey! We are on Facebook now! »