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

Great icosahedron

Index 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. [1]

27 relations: Cambridge University Press, Convex polytope, Coxeter–Dynkin diagram, Density (polytope), Geometry, Great dodecahedron, Great icosidodecahedron, Great stellated dodecahedron, Harold Scott MacDonald Coxeter, Icosahedron, Kepler–Poinsot polyhedron, Net (polyhedron), Omnitruncation, Pentagram, Regular icosahedron, Regular Polytopes (book), Schläfli symbol, Small complex icosidodecahedron, Small stellated dodecahedron, Spherical polyhedron, Stellation, Stellation diagram, Tetrahedral symmetry, Truncated great icosahedron, Truncated octahedron, Truncation (geometry), Vertex arrangement.

Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

New!!: Great icosahedron and Cambridge University Press · See more »

Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.

New!!: Great icosahedron and Convex polytope · 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).

New!!: Great icosahedron and Coxeter–Dynkin diagram · See more »

Density (polytope)

In geometry, the density of a polytope represents the number of windings of a polytope, particularly a uniform or regular polytope, around its center.

New!!: Great icosahedron and Density (polytope) · See more »

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.

New!!: Great icosahedron and Geometry · See more »

Great dodecahedron

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

New!!: Great icosahedron and Great dodecahedron · See more »

Great icosidodecahedron

In geometry, the great icosidodecahedron is a nonconvex uniform polyhedron, indexed as U54.

New!!: Great icosahedron and Great icosidodecahedron · See more »

Great stellated dodecahedron

In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol.

New!!: Great icosahedron and Great stellated dodecahedron · See more »

Harold Scott MacDonald Coxeter

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

New!!: Great icosahedron and Harold Scott MacDonald Coxeter · See more »

Icosahedron

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

New!!: Great icosahedron and Icosahedron · See more »

Kepler–Poinsot polyhedron

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

New!!: Great icosahedron and Kepler–Poinsot polyhedron · See more »

Net (polyhedron)

In geometry a net of a polyhedron is an arrangement of edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron.

New!!: Great icosahedron and Net (polyhedron) · See more »

Omnitruncation

In geometry, an omnitruncation is an operation applied to a regular polytope (or honeycomb) in a Wythoff construction that creates a maximum number of facets.

New!!: Great icosahedron and Omnitruncation · See more »

Pentagram

A pentagram (sometimes known as a pentalpha or pentangle or a star pentagon) is the shape of a five-pointed star drawn with five straight strokes.

New!!: Great icosahedron and Pentagram · See more »

Regular icosahedron

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

New!!: Great icosahedron and Regular icosahedron · See more »

Regular Polytopes (book)

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

New!!: Great icosahedron and Regular Polytopes (book) · See more »

Schläfli symbol

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

New!!: Great icosahedron and Schläfli symbol · See more »

Small complex icosidodecahedron

In geometry, the small complex icosidodecahedron is a degenerate uniform star polyhedron.

New!!: Great icosahedron and Small complex icosidodecahedron · See more »

Small stellated dodecahedron

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

New!!: Great icosahedron and Small stellated dodecahedron · See more »

Spherical polyhedron

In mathematics, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons.

New!!: Great icosahedron and Spherical polyhedron · See more »

Stellation

In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure.

New!!: Great icosahedron and Stellation · See more »

Stellation diagram

In geometry, a stellation diagram or stellation pattern is a two-dimensional diagram in the plane of some face of a polyhedron, showing lines where other face planes intersect with this one.

New!!: Great icosahedron and Stellation diagram · 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.

New!!: Great icosahedron and Tetrahedral symmetry · See more »

Truncated great icosahedron

In geometry, the truncated great icosahedron is a nonconvex uniform polyhedron, indexed as U55.

New!!: Great icosahedron and Truncated great icosahedron · See more »

Truncated octahedron

In geometry, the truncated octahedron is an Archimedean solid.

New!!: Great icosahedron and Truncated octahedron · See more »

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.

New!!: Great icosahedron and Truncation (geometry) · See more »

Vertex arrangement

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

New!!: Great icosahedron and Vertex arrangement · See more »

Redirects here:

Gike, Retrosnub tetrahedron, Retrosnub tetratetrahedron, Sixteenth stellation of icosahedron, Wenninger model index 41.

References

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

OutgoingIncoming
Hey! We are on Facebook now! »