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# 5-orthoplex and Hyperrectangle

## Difference between 5-orthoplex and Hyperrectangle

### 5-orthoplex vs. Hyperrectangle

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, 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.

## Similarities between 5-orthoplex and Hyperrectangle

5-orthoplex and Hyperrectangle have 10 things in common (in Unionpedia): Convex polytope, Coxeter notation, Coxeter–Dynkin diagram, Cross-polytope, Dual polyhedron, Facet (geometry), Geometry, Hypercube, Schläfli symbol, Vertex (geometry).

### 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 notation

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

### 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.

### Dual polyhedron

In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other.

### 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.

### 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.

### Hypercube

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

### 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.

### The list above answers the following questions

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

## 5-orthoplex and Hyperrectangle Comparison

5-orthoplex has 36 relations, while Hyperrectangle has 27. As they have in common 10, the Jaccard index is 15.87% = 10 / (36 + 27).

## References

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

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