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Let $\Pi$ denote the McMullen polytope algebra (over the field of rationals $\mathbb{Q}$) generated by convex polytopes with rational vertices in $\mathbb{R}^n$. For a simple polytope $P$ let us ...

Let $V=\Bbb R^n$. Morelli defined the (commutative unital) ring $L(V)$ to be the additive group generated by the indicator functions of convex polytopes in $V$ with multiplication induced by Minkowski ...

The convex polytope flag vector ring $\mathcal{R}$ satisfies the cone product formula $$ C(U) C(V) = C(J(U, V)) + DUV $$ where $$ J(U, V) = U C(V) + C(U) V - e_1 UV $$ is the join formula. Note: ...

This is related to another question of mine Let $V=\Bbb R^n$. Morelli defined the (commutative unital) ring $L(V)$ to be the additive group generated by the indicator functions of convex polytopes in ...