Cones and convex bodies with modular face lattices (Q2846858)

The authors study a class of convex bodies for which the lattices of their faces are modular. The main result of the paper isNEWLINENEWLINE{Theorem 3.} If \( C \) is a closed convex set in \( {\mathbb R}^n \) whose faces determine an affine space, then there is a face-preserving homeomorphism from \( C \) to a ``parabolic section'' of a cone of positive-semidefinite Hermitian matrices over \( {\mathbb R} \), \( {\mathbb C} \), or \( {\mathbb H} \), or \( C \) has dimension \(8\), \(14\) or \(26\).