|
gptkbp:instanceOf
|
Geometric object
|
|
gptkbp:characterizedBy
|
Schläfli symbol
|
|
gptkbp:definedIn
|
Combinatorial regularity
Geometric regularity
|
|
gptkbp:dimensions
|
n-dimensional
|
|
gptkbp:example
|
gptkb:Octahedron
gptkb:600-cell
gptkb:Tetrahedron
gptkb:Star_polytope
gptkb:Cube
gptkb:120-cell
gptkb:16-cell
gptkb:24-cell
gptkb:5-cell
gptkb:8-cell
gptkb:Dodecahedron
gptkb:Great_dodecahedron
gptkb:Great_icosahedron
gptkb:Great_stellated_dodecahedron
gptkb:Icosahedron
gptkb:Regular_pentagon
gptkb:Small_stellated_dodecahedron
|
|
gptkbp:field
|
gptkb:Mathematics
gptkb:geometry
|
|
gptkbp:generalizes
|
gptkb:Regular_polygon
Platonic solid
Regular polyhedron
|
|
gptkbp:hasDual
|
gptkb:Regular_polytope
|
|
gptkbp:hasProperty
|
Vertex figures are regular polytopes of one lower dimension
All elements are equivalent under symmetry
All facets are regular
All vertex figures are regular
Can be abstract or geometric
Can be convex or non-convex
Faces are regular polytopes of one lower dimension
Finite or infinite
Highly symmetric
Transitive on flags
|
|
gptkbp:hasType
|
gptkb:Abstract_regular_polytope
gptkb:Convex_regular_polytope
gptkb:Star_regular_polytope
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Regular polytope
|
|
gptkbp:includes
|
gptkb:Regular_4-polytope
gptkb:Regular_n-polytope
gptkb:Regular_polygon
Regular polyhedron
|
|
gptkbp:studiedBy
|
gptkb:Ludwig_Schläfli
|
|
gptkbp:symmetry
|
Symmetry group acts transitively on flags
|
|
gptkbp:bfsParent
|
gptkb:Polygon
|
|
gptkbp:bfsLayer
|
5
|