In the

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

of hyperbolic 4-space, the great 120-cell honeycomb is one of four regular star- honeycombs. With

Schläfli symbol In geometry, the Schläfli symbol is a notation of the form \ that defines regular polytopes and tessellations. The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, who generalized Euclidean geometry to more ...

, it has three

great 120-cell In geometry, the great 120-cell or great polydodecahedron is a regular star 4-polytope with Schläfli symbol . It is one of 10 regular Schläfli-Hess polytopes. It is one of the two such polytopes that is self-dual. Related polytopes It has ...

s around each face. It is

dual Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality *** see more cases in :Duality theories * Dual (grammatical ...

to the

order-5 icosahedral 120-cell honeycomb In the geometry of hyperbolic 4-space, the order-5 icosahedral 120-cell honeycomb is one of four regular star- honeycombs. With Schläfli symbol , it has five icosahedral 120-cells around each face. It is dual to the great 120-cell honeycomb. I ...

. It can be seen as a greatening of the

120-cell honeycomb In the geometry of hyperbolic 4-space, the 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol , it has three 120-cells around each face. Its dual is the order-5 5-cell honeycomb, ...

, and is thus analogous to the three-dimensional great dodecahedron and four-dimensional

. It has

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

10.

References

* Coxeter, '' Regular Polytopes'', 3rd. ed., Dover Publications, 1973. . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296) * Coxeter, ''The Beauty of Geometry: Twelve Essays'', Dover Publications, 1999 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213) {{geometry-stub Honeycombs (geometry) 5-polytopes

See also

References