8-demicube

In geometry, a demiocteract or 8-demicube is a uniform 8-polytope, constructed from the 8-hypercube, octeract, with alternated vertices removed. ^[1]

31 relations: Alternation (geometry), Cartesian coordinate system, Convex polytope, Coxeter notation, Coxeter–Dynkin diagram, Demihypercube, Emanuel Lodewijk Elte, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Hypercube, John Horton Conway, Petrie polygon, Rectified 7-simplexes, Regular Polytopes (book), Schläfli symbol, Tetrahedron, Triangle, Uniform 8-polytope, Uniform polytope, Vertex figure, 16-cell, 2 51 honeycomb, 5-cell, 5-demicube, 5-simplex, 6-demicube, 6-simplex, 7-demicube, 7-simplex, 8-cube.
8-polytopes

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.

See 8-demicube and Alternation (geometry)

In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.

See 8-demicube and Cartesian coordinate system

Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n.

See 8-demicube and Convex polytope

Coxeter notation

In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.

See 8-demicube and Coxeter notation

Coxeter–Dynkin diagram

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group.

See 8-demicube and Coxeter–Dynkin diagram

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.

See 8-demicube and Demihypercube

Emanuel Lodewijk Elte

Emanuel Lodewijk Elte (16 March 1881 in Amsterdam – 9 April 1943 in Sobibór) at joodsmonument.nl was a Dutch mathematician.

See 8-demicube and Emanuel Lodewijk Elte

Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

See 8-demicube and Geometry

Gosset–Elte figures

In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated by a Wythoff construction with mirrors all related by order-2 and order-3 dihedral angles.

See 8-demicube and Gosset–Elte figures

Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter (9 February 1907 – 31 March 2003) was a British-Canadian geometer and mathematician.

See 8-demicube and Harold Scott MacDonald Coxeter

Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

See 8-demicube and Hypercube

John Horton Conway

John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

See 8-demicube and John Horton Conway

Petrie polygon

In geometry, a Petrie polygon for a regular polytope of dimensions is a skew polygon in which every consecutive sides (but no) belongs to one of the facets.

See 8-demicube and Petrie polygon

Rectified 7-simplexes

In seven-dimensional geometry, a rectified 7-simplex is a convex uniform 7-polytope, being a rectification of the regular 7-simplex.

See 8-demicube and Rectified 7-simplexes

Regular Polytopes (book)

Regular Polytopes is a geometry book on regular polytopes written by Harold Scott MacDonald Coxeter.

See 8-demicube and Regular Polytopes (book)

Schläfli symbol

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

See 8-demicube and Schläfli symbol

Tetrahedron

In geometry, a tetrahedron (tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices.

See 8-demicube and Tetrahedron

Triangle

A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry.

See 8-demicube and Triangle

Uniform 8-polytope

In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets. 8-demicube and Uniform 8-polytope are 8-polytopes.

See 8-demicube and Uniform 8-polytope

Uniform polytope

In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.

See 8-demicube and Uniform polytope

Vertex figure

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

See 8-demicube and Vertex figure

16-cell

In geometry, the 16-cell is the regular convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

See 8-demicube and 16-cell

2 51 honeycomb

In 8-dimensional geometry, the 251 honeycomb is a space-filling uniform tessellation.

See 8-demicube and 2 51 honeycomb

5-cell

In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol.

See 8-demicube and 5-cell

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.

See 8-demicube and 5-demicube

5-simplex

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.

See 8-demicube and 5-simplex

6-demicube

In geometry, a 6-demicube or demihexeract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.

See 8-demicube and 6-demicube

6-simplex

In geometry, a 6-simplex is a self-dual regular 6-polytope.

See 8-demicube and 6-simplex

7-demicube

In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed.

See 8-demicube and 7-demicube

7-simplex

In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope.

See 8-demicube and 7-simplex

8-cube

In geometry, an 8-cube is an eight-dimensional hypercube. 8-demicube and 8-cube are 8-polytopes.

See 8-demicube and 8-cube

References

[1] https://en.wikipedia.org/wiki/8-demicube

Also known as 1 51 polytope, 8-demihypercube, Demiocteract.

Unionpedia is a concept map or semantic network organized like an encyclopedia – dictionary. It gives a brief definition of each concept and its relationships.

This is a giant online mental map that serves as a basis for concept diagrams. It's free to use and each article or document can be downloaded. It's a tool, resource or reference for study, research, education, learning or teaching, that can be used by teachers, educators, pupils or students; for the academic world: for school, primary, secondary, high school, middle, technical degree, college, university, undergraduate, master's or doctoral degrees; for papers, reports, projects, ideas, documentation, surveys, summaries, or thesis. Here is the definition, explanation, description, or the meaning of each significant on which you need information, and a list of their associated concepts as a glossary. Available in English, Spanish, Portuguese, Japanese, Chinese, French, German, Italian, Polish, Dutch, Russian, Arabic, Hindi, Swedish, Ukrainian, Hungarian, Catalan, Czech, Hebrew, Danish, Finnish, Indonesian, Norwegian, Romanian, Turkish, Vietnamese, Korean, Thai, Greek, Bulgarian, Croatian, Slovak, Lithuanian, Filipino, Latvian, Estonian and Slovenian. More languages soon.

The information is based on Wikipedia articles and other Wikimedia projects, and it's available under the Creative Commons Attribution-ShareAlike License.

Unionpedia is not endorsed by or affiliated with the Wikimedia Foundation.

Google Play, Android and the Google Play logo are trademarks of Google Inc.