Models of some Stellated 4-Polytopes

Abstract

Dans cet article, des modèles de trois 4-polytopes étoilés réguliers, {5/2, 5, 3}, (5, 5/2, 2) et {5/2, 3, 3}, sont construits comme des analogues quadri-dimensionnels de {5/2, S}, (5, 5/2} et {5/2, 3) en trois dimensions. Ils sont tous obtenus par I’étoilement de la cellule-120. De plus, un modèle de I’hyper stella octangula est également construit comme I’analogue quadri-dimensionnel du stella octangula de Kepler, un des composés reguliers. On I’obtient par I’étoilement de la cellule-24.

In this paper, models of three regular star 4-polytopes, {5/2, 5, 3}, (5, 5/2, 3}, and {5/2, 3, 3}, are constructed as 4-dimensional analogues of {5/2, S}, { 5, 5/2}, and {5/2, 3) in 3-space. All of them are obtained from the stellation of the 120-cell. Further, a model of the hyper stella octangula is also constructed as the 4-dimensional analogue of the Kepler’s stella octangula, one of the regular compounds. This is obtained from the stellation of the 24-cell.