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# 5-orthoplex and 5-polytope

## Difference between 5-orthoplex and 5-polytope

### 5-orthoplex vs. 5-polytope

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

## Similarities between 5-orthoplex and 5-polytope

5-orthoplex and 5-polytope have 14 things in common (in Unionpedia): Convex polytope, Coxeter group, Coxeter–Dynkin diagram, Edge (geometry), Face (geometry), Facet (geometry), Geometry, Harold Scott MacDonald Coxeter, Norman Johnson (mathematician), Petrie polygon, Schläfli symbol, Vertex (geometry), Vertex figure, 5-cube.

### 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 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).

### 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).

### 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.

### 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.

### Harold Scott MacDonald Coxeter

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

### Norman Johnson (mathematician)

Norman W. Johnson (born November 12, 1930) is a mathematician, previously at Wheaton College, Norton, Massachusetts.

### 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.

### 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.

### Vertex figure

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

### 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.

### The list above answers the following questions

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

## 5-orthoplex and 5-polytope Comparison

5-orthoplex has 36 relations, while 5-polytope has 50. As they have in common 14, the Jaccard index is 16.28% = 14 / (36 + 50).

## References

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

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