Great grand 120-cell
Encyclopedia
Great grand 120-cell

Orthogonal projection
Type Schläfli-Hess polychoron
Cells 120 {5,5/2}
Faces 720 {5}
Pentagon
In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The sum of the internal angles in a simple pentagon is 540°. A pentagram is an example of a self-intersecting pentagon.- Regular pentagons :In a regular pentagon, all sides are equal in length and...

Edges 1200
Vertices 120
Vertex figure
Vertex figure
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...

{5/2,3}
Schläfli symbol {5,5/2,3}
Coxeter-Dynkin diagram
Coxeter-Dynkin diagram
In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors...

Symmetry group
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 mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example...

H4, [3,3,5]
Dual Great icosahedral 120-cell
Properties

In geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the great grand 120-cell is a star polychoron with Schläfli symbol {5,5/2,3}. It is one of 10 regular Schläfli-Hess polychora.

See also

  • List of regular polytopes
  • Convex regular 4-polytope
    Convex regular 4-polytope
    In mathematics, a convex regular 4-polytope is a 4-dimensional polytope that is both regular and convex. These are the four-dimensional analogs of the Platonic solids and the regular polygons ....

     - Set of convex regular polychoron
  • Kepler-Poinsot polyhedron - regular star polyhedron
    Star polyhedron
    In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality.There are two general kinds of star polyhedron:*Polyhedra which self-intersect in a repetitive way....

  • Star polygon - regular star polygons

External links

The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK