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gptkbp:instanceOf
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Geometric concept
|
|
gptkbp:application
|
gptkb:Crystallography
gptkb:Theoretical_physics
Mathematical art
|
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gptkbp:characterizedBy
|
Schläfli symbol
Symmetry group
|
|
gptkbp:class
|
3 in 1D
3 in dimensions 5 and higher
5 in 3D (Platonic solids)
6 in 4D
Finite number in each dimension
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|
gptkbp:definedIn
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All edges are equivalent
All faces are congruent regular polygons
All vertices are equivalent
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gptkbp:dimensions
|
n-dimensional
|
|
gptkbp:generalizes
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Abstract polytopes
|
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gptkbp:hasDual
|
Dual regular polytope
|
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gptkbp:hasStarForm
|
gptkb:Schläfli–Hess_polychora
gptkb:Kepler–Poinsot_polyhedra
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Regular polytopes
|
|
gptkbp:includes
|
gptkb:Platonic_solids
gptkb:Regular_polyhedra
gptkb:Regular_4-polytopes
gptkb:Regular_polygons
Regular n-polytopes
|
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gptkbp:namedFor
|
gptkb:Ludwig_Schläfli
|
|
gptkbp:notableExample
|
gptkb:Octahedron
gptkb:600-cell
gptkb:Tetrahedron
gptkb:Cube
gptkb:120-cell
gptkb:16-cell
gptkb:24-cell
gptkb:5-cell
gptkb:Dodecahedron
gptkb:Icosahedron
gptkb:Regular_pentagon
Regular hexagon
|
|
gptkbp:property
|
Convex or star-shaped
Highly symmetric
|
|
gptkbp:relatedTo
|
gptkb:Archimedean_solids
Uniform polytopes
|
|
gptkbp:studiedBy
|
gptkb:Euclid
gptkb:Ludwig_Schläfli
|
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gptkbp:studiedIn
|
gptkb:Mathematics
gptkb:geometry
|
|
gptkbp:bfsParent
|
gptkb:Polytopes
|
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gptkbp:bfsLayer
|
7
|