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38 relations: Alternated hypercubic honeycomb, Alternation (geometry), Coxeter group, Coxeter–Dynkin diagram, Cube, Cubic crystal system, Euclidean geometry, Facet (geometry), Four-dimensional space, Harold Scott MacDonald Coxeter, Honeycomb (geometry), Isogonal figure, Isohedral figure, Isotoxal figure, Kissing number problem, Perspective (graphical), Regular Polytopes (book), Schläfli symbol, Snub 24-cell honeycomb, Sphere packing, Tessellation, Tesseractic honeycomb, Tetrahedral-octahedral honeycomb, Tetrahedron, Triangle, Truncated 24-cell honeycomb, Uniform 5-polytope, Vertex arrangement, Vertex figure, Voronoi diagram, 16-cell, 16-cell honeycomb, 24-cell, 24-cell honeycomb, 3-sphere, 5-cell honeycomb, 5-orthoplex, 5-orthoplex honeycomb.
Alternated hypercubic honeycomb
In geometry, the alternated hypercube honeycomb (or demicubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb with an alternation operation.
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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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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 crystal system
In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube.
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Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
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Facet (geometry)
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
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Four-dimensional space
A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D space.
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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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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.
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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.
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Isohedral figure
In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.
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Isotoxal figure
In geometry, a polytope (for example, a polygon or a polyhedron), or a tiling, is isotoxal or edge-transitive if its symmetries act transitively on its edges.
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Kissing number problem
In geometry, a kissing number is defined as the number of non-overlapping unit spheres that can be arranged such that they each touch another given unit sphere.
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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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Regular Polytopes (book)
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
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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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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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Sphere packing
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space.
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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.
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Tesseractic honeycomb
In four-dimensional euclidean geometry, the tesseractic honeycomb is one of the three regular space-filling tessellations (or honeycombs), represented by Schläfli symbol, and constructed by a 4-dimensional packing of tesseract facets.
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Tetrahedral-octahedral honeycomb
The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space.
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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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Truncated 24-cell honeycomb
In four-dimensional Euclidean geometry, the truncated 24-cell honeycomb is a uniform space-filling honeycomb.
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Uniform 5-polytope
In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.
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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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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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Voronoi diagram
In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.
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16-cell
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
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16-cell honeycomb
In four-dimensional Euclidean geometry, the 16-cell honeycomb is one of the three regular space-filling tessellations (or honeycombs) in Euclidean 4-space.
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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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24-cell honeycomb
In four-dimensional Euclidean geometry, the 24-cell honeycomb, or icositetrachoric honeycomb is a regular space-filling tessellation (or honeycomb) of 4-dimensional Euclidean space by regular 24-cells.
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3-sphere
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.
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5-cell honeycomb
In four-dimensional Euclidean geometry, the 4-simplex honeycomb, 5-cell honeycomb or pentachoric-dispentachoric honeycomb is a space-filling tessellation honeycomb.
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5-orthoplex
In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces.
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5-orthoplex honeycomb
In the geometry of hyperbolic 5-space, the 5-orthoplex honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs).
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16-cell tetracomb, 4-demicube honeycomb, 4-demicubic honeycomb, 4-orthoplex honeycomb, Alternated tesseractic honeycomb, Alternated tesserectic honeycomb, D4 lattice, Demitesseractic honeycomb, Demitesseractic tetracomb, Hexadecachoric honeycomb, Hexadecachoric tetracomb, Hexadecachoronic honeycomb, Hexadecachoronic tetracomb.
References
[1] https://en.wikipedia.org/wiki/16-cell_honeycomb
