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Compound of two icosahedra

Index Compound of two icosahedra

This uniform polyhedron compound is a composition of 2 icosahedra. [1]

20 relations: Cartesian coordinate system, Compound of two snub cubes, Compound of two snub dodecahedra, Coxeter–Dynkin diagram, Dodecahedron, Golden ratio, Group action, Icosahedron, Octahedral symmetry, Octahedron, Schläfli symbol, Subgroup, Symmetry group, Tetrahedral symmetry, Triangle, Truncated octahedron, Uniform polyhedron, Uniform polyhedron compound, Vertex arrangement, VRML.

Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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Compound of two snub cubes

This uniform polyhedron compound is a composition of the 2 enantiomers of the snub cube.

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Compound of two snub dodecahedra

This uniform polyhedron compound is a composition of the 2 enantiomers of the snub dodecahedron.

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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).

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Dodecahedron

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

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Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

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Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

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Icosahedron

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

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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.

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Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

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Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

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Subgroup

In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation ∗.

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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.

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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.

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Triangle

A triangle is a polygon with three edges and three vertices.

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Truncated octahedron

In geometry, the truncated octahedron is an Archimedean solid.

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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).

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Uniform polyhedron compound

A uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra, in an arrangement that is also uniform: the symmetry group of the compound acts transitively on the compound's vertices.

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Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions.

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VRML

VRML (Virtual Reality Modeling Language, pronounced vermal or by its initials, originally—before 1995—known as the Virtual Reality Markup Language) is a standard file format for representing 3-dimensional (3D) interactive vector graphics, designed particularly with the World Wide Web in mind.

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Redirects here:

Compound of two dodecahedra, Snub disoctahedron.

References

[1] https://en.wikipedia.org/wiki/Compound_of_two_icosahedra

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