Gosset–Elte figuresIn geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated by a Wythoff construction with mirrors all related by order-2 and order-3 dihedral angles. They can be seen as one-end-ringed Coxeter–Dynkin diagrams. The Coxeter symbol for these figures has the form ki,j, where each letter represents a length of order-3 branches on a Coxeter–Dynkin diagram with a single ring on the end node of a k length sequence of branches.
Demi-hypercubevignette|Les deux demi-hypercubes du cube de dimension 3 sont des tétraèdres. En géométrie, un demi-hypercube est un polytope de dimension n formé en les sommets d'un hypercube de dimension n, c'est-à-dire en ne conservant qu'un sommet sur deux. Il est également appelé polytope de demi-mesure. À partir d'un hypercube donné, on peut obtenir deux demi-hypercubes distincts, en fonction des sommets que l'on élimine et de ceux que l'on garde (il y a deux choix possibles).
Uniform 7-polytopeIn seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Each 5-polytope ridge being shared by exactly two 6-polytope facets. A uniform 7-polytope is one whose symmetry group is transitive on vertices and whose facets are uniform 6-polytopes. Regular 7-polytopes are represented by the Schläfli symbol {p,q,r,s,t,u} with u {p,q,r,s,t} 6-polytopes facets around each 4-face. There are exactly three such convex regular 7-polytopes: {3,3,3,3,3,3} - 7-simplex {4,3,3,3,3,3} - 7-cube {3,3,3,3,3,4} - 7-orthoplex There are no nonconvex regular 7-polytopes.