Two families of locally toroidal regular 4-hypertopes arising from toroids

Infinite families of hypertopes from centrally symmetric polytopes

“…The remaining extra relations of the statement of this corollary come from diagonal classes of improper branches of the diagram G(s). Particularly, when i = 1, we have 4 , a relation given by the type of the polytope. Hence, (ρ…”

“…To prove that the toroidal residue is the map {4, 4} (4,0) , observe that from id = (ρ 0 β −2 ρ 0 β 2 ) 2 we have 4 , showing that the toroidal residue is the map {4, 4} (4,0) .…”

On residual connectedness in chiral geometries

“…Several papers have been written on the subject (see for instance [2,4,5,7,3,8]) and in those papers dealing with chiral hypertopes, the check for residual connectedness has been a bit of a struggle.…”

Locally spherical hypertopes from generalised cubes

“…The concept was introduced in [9] with particular emphasis on regular hypertopes (that is, the ones with highest degree of symmetry). Although in [8,10,11] a number of interesting examples of regular hypertopes have been constructed, within the theory of abstract regular polytopes much more work has been done. Notably, [26] and [28] deal with universal constructions of polytopes, while in [5,23,24] some constructions with prescribed combinatorial conditions are explored.…”