… We begin with the abstract idea of a regular polytope; for convenience we shall follow [3] (…
constructions which are the main tools for our investigation of realizations. Our first construction …

… of regular polytopes and provides a suitable framework for the study of combinatorially regular
… describe a general method for constructing regular incidence-polytopes 9 from groups W, …

… regular polytopes. Naturally, the definitions adopted are designed to generalize those for the
familiar regular polytopes of [5… One possible way of constructing new regular polytopes from …

… an elementary way, constructing such polytopes by building … constructions which relate
different regular polytopes. Thus, … all the cases, that a regular star-polytope must have the same …

… )-polytope whose vertices correspond to regular triangulations of conv(d). In this article we
present three constructions of … , and computational properties of secondary polytopes. The first …

… -construction. Chapter 4 contains lists of known small 2-simple and 2-simplicial 4-polytopes,
of known constructions for such polytopes… in my preprint “New Polytopes from Products” [66]. …

The three aims of this paper are to obtain the proof by Dress of the completeness of the
enumeration of the Grünbaum—Dress polyhedra (that is, the regular apeirohedra, or apeirotopes …

… and geometric operations and constructions on regular polytopes and apeirotopes. … of
regular polytopes; the basic question here asks to what extent the geometry of a regular polytope …

… regular polytope appears in the literature in the context of the construction of regular and “uniform”
polytopes… seen as an instance of “Wythoff’s construction” as described by Coxeter [4, p…

… regular polytope V in a Euclidean space, we will associate a sequence of nonnegative integers
which we shall call regular polytope … the construction of 1-dimensional regular polytope …