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55 relations: Alternation (geometry), Apeirogon, Coxeter group, Coxeter–Dynkin diagram, Cube, Cubic honeycomb, Cuboctahedron, Cuboid, Dodecagon, Dual polyhedron, Face (geometry), Harold Scott MacDonald Coxeter, Hexagon, Hexagonal prism, Hexagonal tiling, Horocycle, Horosphere, Hyperbolic space, Hypercycle (geometry), Ideal point, Jeffrey Weeks (mathematician), List of regular polytopes and compounds, Norman Johnson (mathematician), Octagon, Octahedron, Order-4 apeirogonal tiling, Order-4 dodecahedral honeycomb, Order-6 cubic honeycomb, Paracompact uniform honeycombs, Perspective (graphical), Poincaré disk model, Quasiregular polyhedron, Regular Polytopes (book), Rhombitetrahexagonal tiling, Rhombitrihexagonal tiling, Schläfli symbol, Square, Square pyramid, Tetraapeirogonal tiling, Tetrahedron, Triangle, Triangular cupola, Triangular prism, Triangular tiling, Trihexagonal tiling, Truncated cuboctahedron, Truncated hexagonal tiling, Truncated octahedron, Truncated order-4 apeirogonal tiling, Truncated tetrahedron, ..., Truncated trihexagonal tiling, Uniform honeycombs in hyperbolic space, Vertex figure, Wythoff construction, 16-cell. Expand index (5 more) »
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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Apeirogon
In geometry, an apeirogon (from the Greek word ἄπειρος apeiros, "infinite, boundless" and γωνία gonia, "angle") is a generalized polygon with a countably infinite number of sides.
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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).
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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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Cubic honeycomb
The cubic honeycomb or cubic cellulation is the only regular space-filling tessellation (or honeycomb) in Euclidean 3-space, made up of cubic cells.
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Cuboctahedron
In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.
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Cuboid
In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube.
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Dodecagon
In geometry, a dodecagon or 12-gon is any twelve-sided polygon.
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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.
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Face (geometry)
In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.
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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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Hexagon
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
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Hexagonal prism
In geometry, the hexagonal prism is a prism with hexagonal base.
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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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Horocycle
In hyperbolic geometry, a horocycle (ὅριον + κύκλος — border + circle, sometimes called an oricycle, oricircle, or limit circle) is a curve whose normal or perpendicular geodesics all converge asymptotically in the same direction.
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Horosphere
In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic ''n''-space.
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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.
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Hypercycle (geometry)
In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight line (its axis).
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Ideal point
In hyperbolic geometry, an ideal point, omega point or point at infinity is a well defined point outside the hyperbolic plane or space.
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Jeffrey Weeks (mathematician)
Jeffrey Renwick Weeks (born December 10, 1956) is an American mathematician, a geometric topologist and cosmologist.
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List of regular polytopes and compounds
This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.
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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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Octagon
In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.
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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 apeirogonal tiling
In geometry, the order-4 apeirogonal tiling is a regular tiling of the hyperbolic plane.
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Order-4 dodecahedral honeycomb
In the geometry of hyperbolic 3-space, the order-4 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs).
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Order-6 cubic honeycomb
The order-6 cubic honeycomb is a paracompact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space.
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Paracompact uniform honeycombs
In geometry, uniform honeycombs in hyperbolic space are tessellations of convex uniform polyhedron cells.
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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.
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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.
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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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Regular Polytopes (book)
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
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Rhombitetrahexagonal tiling
In geometry, the rhombitetrahexagonal tiling is a uniform tiling of the hyperbolic plane.
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Rhombitrihexagonal tiling
In geometry, the rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane.
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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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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.
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Square pyramid
In geometry, a square pyramid is a pyramid having a square base.
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Tetraapeirogonal tiling
In geometry, the tetraapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r.
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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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Triangle
A triangle is a polygon with three edges and three vertices.
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Triangular cupola
In geometry, the triangular cupola is one of the Johnson solids (J3).
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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.
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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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Trihexagonal tiling
In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons.
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Truncated cuboctahedron
In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron.
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Truncated hexagonal tiling
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane.
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Truncated octahedron
In geometry, the truncated octahedron is an Archimedean solid.
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Truncated order-4 apeirogonal tiling
In geometry, the truncated order-4 apeirogonal tiling is a uniform tiling of the hyperbolic plane.
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Truncated tetrahedron
In geometry, the truncated tetrahedron is an Archimedean solid.
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Truncated trihexagonal tiling
In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane.
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Uniform honeycombs in hyperbolic space
In hyperbolic geometry, a uniform honeycomb in hyperbolic space is a uniform tessellation of uniform polyhedral cells.
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Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
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Wythoff construction
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.
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16-cell
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
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Redirects here:
Alternated order-4 hexagonal tiling honeycomb, Bitruncated order-4 hexagonal tiling honeycomb, Cantellated order-4 hexagonal tiling honeycomb, Cantic order-4 hexagonal tiling honeycomb, Cantitruncated order-4 hexagonal tiling honeycomb, Omnitruncated order-4 hexagonal tiling honeycomb, Quarter order-4 hexagonal tiling honeycomb, Quarter order-6 cubic honeycomb, Rectified order-4 hexagonal tiling honeycomb, Runcic order-4 hexagonal tiling honeycomb, Runcicantic order-4 hexagonal tiling honeycomb, Runcinated order-4 hexagonal tiling honeycomb, Runcinated order-6 cubic honeycomb, Runcitruncated order-4 hexagonal tiling honeycomb, Truncated order-4 hexagonal tiling honeycomb.
References
[1] https://en.wikipedia.org/wiki/Order-4_hexagonal_tiling_honeycomb
