Order-5 icosahedral 120-cell honeycomb(No image)TypeHyperbolic regular honeycombSchläfli symbol{3,5,5/2,5} Coxeter diagram4-faces {3,5,5/2}Cells {3,5}Faces {3}Face figure {5}Edge figure {5/2,5}Vertex figure {5,5/2,5}DualGreat 120-cell honeycombCoxeter group4, [5,3,3,3]PropertiesRegular In the geometry of hyperbolic 4-space, the order-5 icosahedral 120-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {3,5,5/2,5}, it has five icosahedral 120-cells around each face. Acronym: tifipte
It is dual to the great 120-cell honeycomb.
It can be constructed by replacing the great dodecahedral cells of the great 120-cell honeycomb with their icosahedral convex hulls, thus replacing the great 120-cells with icosahedral 120-cells. It is thus analogous to the four-dimensional icosahedral 120-cell. It has density 10.
See also List of regular polytopes
Notes
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, pp. 212–213) x3o5o5/2o5o - tifipte