In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements (vertices, edges, etc). Equivalently this operation can be imagined by keeping facets in the same location, but reducing their size.
According to Coxeter, this multidimensional term was defined by Alicia Boole Stott for creating new polytopes, specifically starting from regular polytopes constructs ne...
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In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements (vertices, edges, etc). Equivalently this operation can be imagined by keeping facets in the same location, but reducing their size.
According to Coxeter, this multidimensional term was defined by Alicia Boole Stott for creating new polytopes, specifically starting from regular polytopes constructs new uniform polytopes.
The expansion operation is symmetric with respects to a regular polytope and its dual. The resulting figure contains the facets of both the regular and regular dual, along with various prismatic facets filling the gaps created between intermediate dimensional elements.
It has somewhat different meanings by dimension, and correspond to reflections from the first and last mirrors in a Wythoff construction.
By dimension:
The general operator for expansion for an n-polytope is t0,n-1{p,q,r,...}. New simplex facets are added at...
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