Great icosahedral 120-cell
Encyclopedia
Great icosahedral 120-cell

Orthogonal projection
Type Schläfli-Hess polychoron
Cells 120 {3,5/2}
Faces 1200 {3}
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....

Edges 720
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:...

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

Related polytopes

It has the same edge arrangement as the great stellated 120-cell, and grand stellated 120-cell, and face arrangement of the grand 600-cell.

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 solid
    Kepler-Poinsot solid
    In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. They may be obtained by stellating the regular convex dodecahedron and icosahedron, and differ from these in having regular pentagrammic faces or vertex figures....

    s - 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

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