TL;DR
This paper explores the mixing operation for regular convex polytopes, identifying when the resulting structure remains a polytope and detailing its structure in each case.
Contribution
It provides a comprehensive analysis of the mixing operation applied to regular convex polytopes, including conditions for the mix to be a polytope and its detailed structure.
Findings
Identifies conditions under which the mix of two regular convex polytopes is a polytope.
Determines the structure of the mix for all cases of regular convex polytopes.
Provides a complete classification of the mixing operation outcomes.
Abstract
The mixing operation for abstract polytopes gives a natural way to construct the minimal common cover of two polytopes. In this paper, we apply this construction to the regular convex polytopes, determining when the mix is again a polytope, and completely determining the structure of the mix in each case.
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