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# 5-orthoplex and Hypercube

## Difference between 5-orthoplex and Hypercube

### 5-orthoplex vs. Hypercube

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. In geometry, a hypercube is an n-dimensional analogue of a square (n.

## Similarities between 5-orthoplex and Hypercube

5-orthoplex and Hypercube have 16 things in common (in Unionpedia): Cartesian coordinate system, Convex polytope, Coxeter–Dynkin diagram, Cross-polytope, Edge (geometry), Face (geometry), Geometry, Harold Scott MacDonald Coxeter, Hyperrectangle, Perspective (graphical), Petrie polygon, Regular polytope, Schläfli symbol, Vertex (geometry), 5-cube, 5-polytope.

### Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

### Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.

### 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).

### Cross-polytope

In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in any number of dimensions.

### Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

### 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.

### Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

### Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 &ndash; March 31, 2003) was a British-born Canadian geometer.

### Hyperrectangle

In geometry, an n-orthotopeCoxeter, 1973 (also called a hyperrectangle or a box) is the generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.

### Perspective (graphical)

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

### Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon such that every (n-1) consecutive sides (but no n) belong to one of the facets.

### Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry.

### Schläfli symbol

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

### Vertex (geometry)

In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes.

### 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.

### 5-polytope

In five-dimensional geometry, a five-dimensional polytope or 5-polytope is a 5-dimensional polytope, bounded by (4-polytope) facets.

### The list above answers the following questions

• What 5-orthoplex and Hypercube have in common
• What are the similarities between 5-orthoplex and Hypercube

## 5-orthoplex and Hypercube Comparison

5-orthoplex has 36 relations, while Hypercube has 61. As they have in common 16, the Jaccard index is 16.49% = 16 / (36 + 61).

## References

This article shows the relationship between 5-orthoplex and Hypercube. To access each article from which the information was extracted, please visit:

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