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

Icosahedral honeycomb

Index Icosahedral honeycomb

The icosahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. [1]

47 relations: Abstract polytope, Bitruncation, Coxeter group, Coxeter–Dynkin diagram, Decagon, Dihedral angle, Disphenoid, Dodecagon, Dodecahedron, Dual polyhedron, Harold Scott MacDonald Coxeter, Hexagon, Hexagonal prism, Honeycomb (geometry), Hyperbolic space, Icosahedron, Icosidodecahedron, Isogonal figure, Johnson solid, List of regular polytopes and compounds, Norman Johnson (mathematician), Octahedron, Pentagon, Pentagonal antiprism, Pentagonal prism, Perspective (graphical), Poincaré disk model, Pyramid (geometry), Regular 4-polytope, Regular Polytopes (book), Rhombicosidodecahedron, Schläfli symbol, Seifert–Weber space, Snub dodecahedron, Square, Square pyramid, Tessellation, Tetrahedrally diminished dodecahedron, Tetrahedron, Triangle, Triangular prism, Truncated dodecahedron, Truncated icosahedron, Truncated icosidodecahedron, Uniform honeycombs in hyperbolic space, Vertex figure, 11-cell.

Abstract polytope

In mathematics, an abstract polytope is an algebraic partially ordered set or poset which captures the combinatorial properties of a traditional polytope, but not any purely geometric properties such as angles, edge lengths, etc.

New!!: Icosahedral honeycomb and Abstract polytope · See more »

Bitruncation

In geometry, a bitruncation is an operation on regular polytopes.

New!!: Icosahedral honeycomb and Bitruncation · 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).

New!!: Icosahedral honeycomb and Coxeter group · 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!!: Icosahedral honeycomb and Coxeter–Dynkin diagram · See more »

Decagon

In geometry, a decagon is a ten-sided polygon or 10-gon.

New!!: Icosahedral honeycomb and Decagon · See more »

Dihedral angle

A dihedral angle is the angle between two intersecting planes.

New!!: Icosahedral honeycomb and Dihedral angle · See more »

Disphenoid

In geometry, a disphenoid (from Greek sphenoeides, "wedgelike") is a tetrahedron whose four faces are congruent acute-angled triangles.

New!!: Icosahedral honeycomb and Disphenoid · See more »

Dodecagon

In geometry, a dodecagon or 12-gon is any twelve-sided polygon.

New!!: Icosahedral honeycomb and Dodecagon · 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.

New!!: Icosahedral honeycomb and Dodecahedron · 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.

New!!: Icosahedral honeycomb and Dual polyhedron · 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!!: Icosahedral honeycomb and Harold Scott MacDonald Coxeter · See more »

Hexagon

In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

New!!: Icosahedral honeycomb and Hexagon · See more »

Hexagonal prism

In geometry, the hexagonal prism is a prism with hexagonal base.

New!!: Icosahedral honeycomb and Hexagonal prism · See more »

Honeycomb (geometry)

In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps.

New!!: Icosahedral honeycomb and Honeycomb (geometry) · See more »

Hyperbolic space

In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.

New!!: Icosahedral honeycomb and Hyperbolic space · See more »

Icosahedron

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

New!!: Icosahedral honeycomb and Icosahedron · See more »

Icosidodecahedron

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

New!!: Icosahedral honeycomb and Icosidodecahedron · See more »

Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

New!!: Icosahedral honeycomb and Isogonal figure · See more »

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.

New!!: Icosahedral honeycomb and Johnson solid · See more »

List of regular polytopes and compounds

This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.

New!!: Icosahedral honeycomb and List of regular polytopes and compounds · See more »

Norman Johnson (mathematician)

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

New!!: Icosahedral honeycomb and Norman Johnson (mathematician) · See more »

Octahedron

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

New!!: Icosahedral honeycomb and Octahedron · See more »

Pentagon

In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.

New!!: Icosahedral honeycomb and Pentagon · See more »

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.

New!!: Icosahedral honeycomb and Pentagonal antiprism · See more »

Pentagonal prism

In geometry, the pentagonal prism is a prism with a pentagonal base.

New!!: Icosahedral honeycomb and Pentagonal prism · See more »

Perspective (graphical)

Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.

New!!: Icosahedral honeycomb and Perspective (graphical) · See more »

Poincaré disk model

In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which the points of the geometry are inside the unit disk, and the straight lines consist of all segments of circles contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk.

New!!: Icosahedral honeycomb and Poincaré disk model · See more »

Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

New!!: Icosahedral honeycomb and Pyramid (geometry) · See more »

Regular 4-polytope

In mathematics, a regular 4-polytope is a regular four-dimensional polytope.

New!!: Icosahedral honeycomb and Regular 4-polytope · See more »

Regular Polytopes (book)

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

New!!: Icosahedral honeycomb and Regular Polytopes (book) · See more »

Rhombicosidodecahedron

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

New!!: Icosahedral honeycomb and Rhombicosidodecahedron · See more »

Schläfli symbol

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

New!!: Icosahedral honeycomb and Schläfli symbol · See more »

Seifert–Weber space

In mathematics, Seifert–Weber space (introduced by Herbert Seifert and Constantin Weber) is a closed hyperbolic 3-manifold.

New!!: Icosahedral honeycomb and Seifert–Weber space · 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.

New!!: Icosahedral honeycomb and Snub dodecahedron · See more »

Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

New!!: Icosahedral honeycomb and Square · See more »

Square pyramid

In geometry, a square pyramid is a pyramid having a square base.

New!!: Icosahedral honeycomb and Square pyramid · See more »

Tessellation

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.

New!!: Icosahedral honeycomb and Tessellation · See more »

Tetrahedrally diminished dodecahedron

In geometry, a tetrahedrally diminished dodecahedron (also tetrahedrally stellated icosahedron) is a topologically self-dual polyhedron made of 16 vertices, 30 edges, and 16 faces (4 equilateral triangles and 12 identical quadrilaterals).

New!!: Icosahedral honeycomb and Tetrahedrally diminished dodecahedron · See more »

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.

New!!: Icosahedral honeycomb and Tetrahedron · See more »

Triangle

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

New!!: Icosahedral honeycomb and Triangle · See more »

Triangular prism

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

New!!: Icosahedral honeycomb and Triangular prism · See more »

Truncated dodecahedron

In geometry, the truncated dodecahedron is an Archimedean solid.

New!!: Icosahedral honeycomb and Truncated dodecahedron · 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.

New!!: Icosahedral honeycomb and Truncated icosahedron · See more »

Truncated icosidodecahedron

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

New!!: Icosahedral honeycomb and Truncated icosidodecahedron · See more »

Uniform honeycombs in hyperbolic space

In hyperbolic geometry, a uniform honeycomb in hyperbolic space is a uniform tessellation of uniform polyhedral cells.

New!!: Icosahedral honeycomb and Uniform honeycombs in hyperbolic space · See more »

Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

New!!: Icosahedral honeycomb and Vertex figure · See more »

11-cell

In mathematics, the 11-cell (or hendecachoron) is a self-dual abstract regular 4-polytope (four-dimensional polytope).

New!!: Icosahedral honeycomb and 11-cell · See more »

Redirects here:

Bitruncated icosahedral honeycomb, Cantellated icosahedral honeycomb, Cantitruncated icosahedral honeycomb, Hyperbolic icosahedral honeycomb, Omnisnub icosahedral honeycomb, Omnitruncated icosahedral honeycomb, Order-3 icosahedral honeycomb, Partially diminished icosahedral honeycomb, Partially truncated icosahedral honeycomb, Rectified icosahedral honeycomb, Runcinated icosahedral honeycomb, Runcitruncated icosahedral honeycomb, Truncated icosahedral honeycomb.

References

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

OutgoingIncoming
Hey! We are on Facebook now! »