Great grand stellated 120-cell
Encyclopedia
| Great grand stellated 120-cell | |
|---|---|
 Orthogonal projection |
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| Type | Schläfli-Hess polychoron |
| Cells | 120 {5/2,3} |
| Faces | 720 {5/2} Pentagram A pentagram is the shape of a five-pointed star drawn with five straight strokes... |
| Edges | 1200 |
| Vertices | 600 |
| 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:... |
{3,3} Tetrahedron In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids... |
| Schläfli symbol | {5/2,3,3} |
| 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... |
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| 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 | Grand 600-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 stellated 120-cell is a star polychoron with Schläfli symbol {5/2,3,3}. It is one of 10 regular Schläfli-Hess polychora. It is unique among the 10 for having 600 vertices, and has the same vertex arrangement
Vertex arrangement
In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes....
as the regular convex 120-cell.
It is one of four regular star polychora discovered by Ludwig Schläfli
Ludwig Schläfli
Ludwig Schläfli was a Swiss geometer and complex analyst who was one of the key figures in developing the notion of higher dimensional spaces. The concept of multidimensionality has since come to play a pivotal role in physics, and is a common element in science fiction...
. It is named by John Horton Conway
John Horton Conway
John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
, extending the naming system by Arthur Cayley
Arthur Cayley
Arthur Cayley F.R.S. was a British mathematician. He helped found the modern British school of pure mathematics....
for the 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, and the only one containing all three modifiers in the name.
As a stellation
The great grand stellated 120-cell is the final stellationStellation
Stellation is a process of constructing new polygons , new polyhedra in three dimensions, or, in general, new polytopes in n dimensions. The process consists of extending elements such as edges or face planes, usually in a symmetrical way, until they meet each other again...
of the 120-cell, and is the only Schläfli-Hess Polychoron to have the 120-cell for its convex hull.
Images
 A Zome Zome The term zome is used in several related senses. A zome in the original sense is a building using unusual geometries .... model |
 Orthogonal projection as a wireframe |
See also
- List of regular polytopes
- Convex regular 4-polytopeConvex regular 4-polytopeIn 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 solidKepler-Poinsot solidIn 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 polyhedronStar polyhedronIn 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