We provide new polyhedra without diagonals, and we discuss their embeddings in euclidean 3-space with maximal symmetries starting with a complete classification of their combinatorial properties: orientable neighborly 2-pseudomanifolds with 9 vertices or Mendelsohn triple systems S 2(2, 3, 9). This article was motivated by the longstanding and still open question: find a triangulated 2-manifold which can not be embedded in 3-space. Furthermore, we applied tested and improved algorithms for realizing oriented matroids or finding final polynomials.
ASJC Scopus subject areas
- Mathematics (all)