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Platonic solid and Rectified 5-cell

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Platonic solid and Rectified 5-cell

Platonic solid vs. Rectified 5-cell

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells.

Similarities between Platonic solid and Rectified 5-cell

Platonic solid and Rectified 5-cell have 19 things in common (in Unionpedia): Cartesian coordinate system, Cross-polytope, Dual polyhedron, Face (geometry), Isogonal figure, Isotoxal figure, Octahedron, Pentagon, Polyhedral combinatorics, Rectification (geometry), Regular polytope, Schläfli symbol, Simplex, Tetrahedron, Triangle, Vertex figure, Wythoff construction, 24-cell, 5-cell.

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 to the point from two fixed perpendicular directed lines, measured in the same unit of length.

Cartesian coordinate system and Platonic solid · Cartesian coordinate system and Rectified 5-cell · See more »

Cross-polytope

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

Cross-polytope and Platonic solid · Cross-polytope and Rectified 5-cell · See more »

Dual polyhedron

In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

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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.

Face (geometry) and Platonic solid · Face (geometry) and Rectified 5-cell · 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.

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Isotoxal figure

In geometry, a polytope (for example, a polygon or a polyhedron), or a tiling, is isotoxal or edge-transitive if its symmetries act transitively on its edges.

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Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

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Pentagon

In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.

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Polyhedral combinatorics

Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.

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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.

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Regular polytope

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

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Schläfli symbol

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

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Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

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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.

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Triangle

A triangle is a polygon with three edges and three vertices.

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Vertex figure

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

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Wythoff construction

In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.

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24-cell

In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

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5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

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The list above answers the following questions

Platonic solid and Rectified 5-cell Comparison

Platonic solid has 190 relations, while Rectified 5-cell has 53. As they have in common 19, the Jaccard index is 7.82% = 19 / (190 + 53).

References

This article shows the relationship between Platonic solid and Rectified 5-cell. To access each article from which the information was extracted, please visit:

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