80 relations: Alternated hexagonal tiling honeycomb, Alternation (geometry), Antiprism, Apeirogonal antiprism, Archimedean solid, Convex uniform honeycomb, Conway polyhedron notation, Coxeter–Dynkin diagram, Cube, Cuboctahedron, Digon, Dodecahedron, Expansion (geometry), Geometry, Great icosahedron, Great inverted snub icosidodecahedron, Great retrosnub icosidodecahedron, Great snub dodecicosidodecahedron, Great snub icosidodecahedron, Harold Scott MacDonald Coxeter, Heptagonal antiprism, Heptagonal tiling, Hexagonal antiprism, Hexagonal tiling, Hosohedron, Icosahedron, Icosidodecahedron, Inverted snub dodecadodecahedron, Johannes Kepler, John Horton Conway, Johnson solid, Lune (geometry), Norman Johnson (mathematician), Octagonal antiprism, Octahedron, Order-4 octahedral honeycomb, Order-7 triangular tiling, Pentagonal antiprism, Quasiregular polyhedron, Rectification (geometry), Regular polyhedron, Regular Polytopes (book), Runcinated 24-cells, Schläfli symbol, Small retrosnub icosicosidodecahedron, Small snub icosicosidodecahedron, Snub 24-cell, Snub 24-cell honeycomb, Snub apeiroapeirogonal tiling, Snub cube, ..., Snub disphenoid, Snub dodecadodecahedron, Snub dodecahedron, Snub heptaheptagonal tiling, Snub hexahexagonal tiling, Snub icosidodecadodecahedron, Snub octaoctagonal tiling, Snub pentapentagonal tiling, Snub polyhedron, Snub square antiprism, Snub square tiling, Snub tetraapeirogonal tiling, Snub tetraheptagonal tiling, Snub tetrahexagonal tiling, Snub tetraoctagonal tiling, Snub tetrapentagonal tiling, Snub triapeirogonal tiling, Snub triheptagonal tiling, Snub trihexagonal tiling, Snub trioctagonal tiling, Square antiprism, Square tiling, Tetrahedral symmetry, Tetrahedron, Triangular tiling, Truncated 24-cells, Truncated octahedron, Truncation (geometry), Uniform polytope, 24-cell. Expand index (30 more) »

## Alternated hexagonal tiling honeycomb

In 3-dimensional hyperbolic geometry, the alternated hexagonal tiling honeycomb, h, or, with tetrahedron and triangular tiling cells, in an octahedron vertex figure.

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## 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.

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## 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.

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## Apeirogonal antiprism

In geometry, an apeirogonal antiprism or infinite antiprism is the arithmetic limit of the family of antiprisms; it can be considered an infinite polyhedron or a tiling of the plane.

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## Archimedean solid

In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.

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## 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.

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## Conway polyhedron notation

In geometry, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix operations.

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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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## Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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## Cuboctahedron

In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.

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## Digon

In geometry, a digon is a polygon with two sides (edges) and two vertices.

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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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## Expansion (geometry)

In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements (vertices, edges, etc.). Equivalently this operation can be imagined by keeping facets in the same position but reducing their size.

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## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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## 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.

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## Great inverted snub icosidodecahedron

In geometry, the great inverted snub icosidodecahedron is a uniform star polyhedron, indexed as U69.

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## Great retrosnub icosidodecahedron

In geometry, the great retrosnub icosidodecahedron or great inverted retrosnub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U74.

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## Great snub dodecicosidodecahedron

In geometry, the great snub dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U64.

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## Great snub icosidodecahedron

In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U57.

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## Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

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## Heptagonal antiprism

In geometry, the heptagonal antiprism is the fifth in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.

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## Heptagonal tiling

In geometry, the heptagonal tiling is a regular tiling of the hyperbolic plane.

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## Hexagonal antiprism

In geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.

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## Hexagonal tiling

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.

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## Hosohedron

In geometry, an ''n''-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite vertices.

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## Icosahedron

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

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## Icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces.

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## Inverted snub dodecadodecahedron

In geometry, the inverted snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U60.

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## Johannes Kepler

Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.

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## John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

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## Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron, which is not uniform (i.e., not a Platonic solid, Archimedean solid, prism, or antiprism), and each face of which is a regular polygon.

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## Lune (geometry)

In plane geometry, a lune is the concave-convex area bounded by two circular arcs, while a convex-convex area is termed a lens.

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## Norman Johnson (mathematician)

Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.

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## Octagonal antiprism

In geometry, the octagonal antiprism is the 6th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.

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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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## Order-4 octahedral honeycomb

In the geometry of hyperbolic 3-space, the order-4 octahedral honeycomb is a regular paracompact honeycomb.

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## Order-7 triangular tiling

In geometry, the order-7 triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of.

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## Pentagonal antiprism

In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.

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## Quasiregular polyhedron

In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex.

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## Rectification (geometry)

In Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.

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## Regular polyhedron

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.

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## Regular Polytopes (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.

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## Runcinated 24-cells

In four-dimensional geometry, a runcinated 24-cell is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular 24-cell.

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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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## Small retrosnub icosicosidodecahedron

In geometry, the small retrosnub icosicosidodecahedron or small inverted retrosnub icosicosidodecahedron is a nonconvex uniform polyhedron, indexed as U72.

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## Small snub icosicosidodecahedron

In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U32.

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## Snub 24-cell

In geometry, the snub 24-cell or snub disicositetrachoron is a convex uniform 4-polytope composed of 120 regular tetrahedral and 24 icosahedral cells.

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## Snub 24-cell honeycomb

In four-dimensional Euclidean geometry, the snub 24-cell honeycomb, or snub icositetrachoric honeycomb is a uniform space-filling tessellation (or honeycomb) by snub 24-cells, 16-cells, and 5-cells.

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## Snub apeiroapeirogonal tiling

In geometry, the snub apeiroapeirogonal tiling is a uniform tiling of the hyperbolic plane.

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## Snub cube

In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles.

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## Snub disphenoid

In geometry, the snub disphenoid, Siamese dodecahedron, triangular dodecahedron or dodecadeltahedron is a three-dimensional convex polyhedron with twelve equilateral triangles as its faces.

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## Snub dodecadodecahedron

In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U40.

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## 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.

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## Snub heptaheptagonal tiling

In geometry, the snub heptaheptagonal tiling is a uniform tiling of the hyperbolic plane.

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## Snub hexahexagonal tiling

In geometry, the snub hexahexagonal tiling is a uniform tiling of the hyperbolic plane.

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## Snub icosidodecadodecahedron

In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U46.

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## Snub octaoctagonal tiling

In geometry, the snub octaoctagonal tiling is a uniform tiling of the hyperbolic plane.

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## Snub pentapentagonal tiling

In geometry, the snub pentapentagonal tiling is a regular tiling of the hyperbolic plane.

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## Snub polyhedron

A snub polyhedron is a polyhedron obtained by alternating a corresponding omnitruncated or truncated polyhedron, depending on the definition.

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## Snub square antiprism

In geometry, the snub square antiprism is one of the Johnson solids (J85).

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## Snub square tiling

In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane.

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## Snub tetraapeirogonal tiling

In geometry, the snub tetrapeirogonal tiling is a uniform tiling of the hyperbolic plane.

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## Snub tetraheptagonal tiling

In geometry, the snub tetraheptagonal tiling is a uniform tiling of the hyperbolic plane.

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## Snub tetrahexagonal tiling

In geometry, the snub tetrahexagonal tiling is a uniform tiling of the hyperbolic plane.

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## Snub tetraoctagonal tiling

In geometry, the snub tetraoctagonal tiling is a uniform tiling of the hyperbolic plane.

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## Snub tetrapentagonal tiling

In geometry, the snub tetrapentagonal tiling is a uniform tiling of the hyperbolic plane.

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## Snub triapeirogonal tiling

In geometry, the snub triapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of sr.

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## Snub triheptagonal tiling

In geometry, the order-3 snub heptagonal tiling is a semiregular tiling of the hyperbolic plane.

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## Snub trihexagonal tiling

In geometry, the snub hexagonal tiling (or snub trihexagonal tiling) is a semiregular tiling of the Euclidean plane.

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## Snub trioctagonal tiling

In geometry, the order-3 snub octagonal tiling is a semiregular tiling of the hyperbolic plane.

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## Square antiprism

In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.

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## Square tiling

In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.

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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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## 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.

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## Triangular tiling

In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.

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## Truncated 24-cells

In geometry, a truncated 24-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 24-cell.

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## Truncated octahedron

In geometry, the truncated octahedron is an Archimedean solid.

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## Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.

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## Uniform polytope

A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.

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## 24-cell

In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

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## Redirects here:

## References

[1] https://en.wikipedia.org/wiki/Snub_(geometry)