Faster access than browser!
51 relations: Catalan solid, Chamfer (geometry), Chamfered dodecahedron, Conway polyhedron notation, Cube, Cubic honeycomb, Demihypercube, Digon, Harold Scott MacDonald Coxeter, Honeycomb (geometry), Hypercube, Isogonal figure, Norman Johnson (mathematician), Polygon, Polyhedron, Polytope, Polytope compound, Quasiregular polyhedron, Rectification (geometry), Regular Polytopes (book), Rhombic dodecahedron, Rhombic triacontahedron, Small ditrigonal icosidodecahedron, Snub 24-cell, Snub 24-cell honeycomb, Snub cube, Snub square antiprism, Square antiprism, Star polyhedron, Stellated octahedron, Tessellation, Tesseract, Tetrahedral-octahedral honeycomb, Tetrahedron, Triakis icosahedron, Triakis octahedron, Triakis tetrahedron, Triangular prismatic honeycomb, Truncated 24-cell honeycomb, Truncated 24-cells, Truncated cuboctahedron, Truncated triakis tetrahedron, Truncation (geometry), Vertex configuration, Wythoff construction, 16-cell, 4-polytope, 5-cube, 5-demicube, 6-cube, ..., 6-demicube. Expand index (1 more) »
Catalan solid
In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid.
New!!: Alternation (geometry) and Catalan solid · See more »
Chamfer (geometry)
In geometry, chamfering or edge-truncation is a topological operator that modifies one polyhedron into another.
New!!: Alternation (geometry) and Chamfer (geometry) · See more »
Chamfered dodecahedron
The chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 30 hexagons and 12 pentagons.
New!!: Alternation (geometry) and Chamfered dodecahedron · See more »
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.
New!!: Alternation (geometry) and Conway polyhedron notation · See more »
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.
New!!: Alternation (geometry) and Cube · See more »
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.
New!!: Alternation (geometry) and Cubic honeycomb · See more »
Demihypercube
In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as hγn for being half of the hypercube family, γn.
New!!: Alternation (geometry) and Demihypercube · See more »
Digon
In geometry, a digon is a polygon with two sides (edges) and two vertices.
New!!: Alternation (geometry) and Digon · 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!!: Alternation (geometry) and Harold Scott MacDonald Coxeter · 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!!: Alternation (geometry) and Honeycomb (geometry) · See more »
Hypercube
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
New!!: Alternation (geometry) and Hypercube · 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!!: Alternation (geometry) and Isogonal figure · See more »
Norman Johnson (mathematician)
Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.
New!!: Alternation (geometry) and Norman Johnson (mathematician) · See more »
Polygon
In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
New!!: Alternation (geometry) and Polygon · See more »
Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
New!!: Alternation (geometry) and Polyhedron · See more »
Polytope
In elementary geometry, a polytope is a geometric object with "flat" sides.
New!!: Alternation (geometry) and Polytope · See more »
Polytope compound
A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.
New!!: Alternation (geometry) and Polytope compound · See more »
Quasiregular polyhedron
In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex.
New!!: Alternation (geometry) and Quasiregular polyhedron · See more »
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.
New!!: Alternation (geometry) and Rectification (geometry) · See more »
Regular Polytopes (book)
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
New!!: Alternation (geometry) and Regular Polytopes (book) · See more »
Rhombic dodecahedron
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces.
New!!: Alternation (geometry) and Rhombic dodecahedron · See more »
Rhombic triacontahedron
In geometry, the rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces.
New!!: Alternation (geometry) and Rhombic triacontahedron · See more »
Small ditrigonal icosidodecahedron
In geometry, the small ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U30.
New!!: Alternation (geometry) and Small ditrigonal icosidodecahedron · See more »
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.
New!!: Alternation (geometry) and Snub 24-cell · See more »
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.
New!!: Alternation (geometry) and Snub 24-cell honeycomb · See more »
Snub cube
In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles.
New!!: Alternation (geometry) and Snub cube · See more »
Snub square antiprism
In geometry, the snub square antiprism is one of the Johnson solids (J85).
New!!: Alternation (geometry) and Snub square antiprism · See more »
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.
New!!: Alternation (geometry) and Square antiprism · See more »
Star polyhedron
In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality.
New!!: Alternation (geometry) and Star polyhedron · See more »
Stellated octahedron
The stellated octahedron is the only stellation of the octahedron.
New!!: Alternation (geometry) and Stellated octahedron · 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!!: Alternation (geometry) and Tessellation · See more »
Tesseract
In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.
New!!: Alternation (geometry) and Tesseract · See more »
Tetrahedral-octahedral honeycomb
The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space.
New!!: Alternation (geometry) and Tetrahedral-octahedral honeycomb · 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!!: Alternation (geometry) and Tetrahedron · See more »
Triakis icosahedron
In geometry, the triakis icosahedron (or kisicosahedron) is an Archimedean dual solid, or a Catalan solid.
New!!: Alternation (geometry) and Triakis icosahedron · See more »
Triakis octahedron
In geometry, a triakis octahedron (or trigonal trisoctahedron or kisoctahedron) is an Archimedean dual solid, or a Catalan solid.
New!!: Alternation (geometry) and Triakis octahedron · See more »
Triakis tetrahedron
In geometry, a triakis tetrahedron (or kistetrahedron) is an Archimedean dual solid, or a Catalan solid.
New!!: Alternation (geometry) and Triakis tetrahedron · See more »
Triangular prismatic honeycomb
The triangular prismatic honeycomb or triangular prismatic cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space.
New!!: Alternation (geometry) and Triangular prismatic honeycomb · See more »
Truncated 24-cell honeycomb
In four-dimensional Euclidean geometry, the truncated 24-cell honeycomb is a uniform space-filling honeycomb.
New!!: Alternation (geometry) and Truncated 24-cell honeycomb · See more »
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.
New!!: Alternation (geometry) and Truncated 24-cells · See more »
Truncated cuboctahedron
In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron.
New!!: Alternation (geometry) and Truncated cuboctahedron · See more »
Truncated triakis tetrahedron
The truncated triakis tetrahedron is a convex polyhedron with 16 faces: 4 sets of 3 pentagons arranged in a tetrahedral arrangement, with 4 hexagons in the gaps.
New!!: Alternation (geometry) and Truncated triakis tetrahedron · 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!!: Alternation (geometry) and Truncation (geometry) · See more »
Vertex configuration
In geometry, a vertex configuration by Walter Steurer, Sofia Deloudi, (2009) pp.
New!!: Alternation (geometry) and Vertex configuration · See more »
Wythoff construction
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.
New!!: Alternation (geometry) and Wythoff construction · See more »
16-cell
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
New!!: Alternation (geometry) and 16-cell · See more »
4-polytope
In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope.
New!!: Alternation (geometry) and 4-polytope · See more »
5-cube
In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces.
New!!: Alternation (geometry) and 5-cube · See more »
5-demicube
In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed.
New!!: Alternation (geometry) and 5-demicube · See more »
6-cube
In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.
New!!: Alternation (geometry) and 6-cube · See more »
6-demicube
In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.
New!!: Alternation (geometry) and 6-demicube · See more »
Redirects here:
Altered (geometry), Simiation, Snubification.
References
[1] https://en.wikipedia.org/wiki/Alternation_(geometry)
