Toroidal polyhedra are polyhedral structures that are topologically equivalent to a torus, meaning they have a shape resembling a doughnut. In mathematical terms, a toroidal structure has a genus of one, indicating it has one hole.
The Császár polyhedron is a non-convex polyhedron that is a type of self-intersecting figure. It is characterized by its unique properties regarding its vertices, edges, and faces. The Császár polyhedron has 14 faces, 28 edges, and 14 vertices. Importantly, its faces consist of two types: quadrilateral and triaugmented triangular prisms.
The Great Dodecahedron is one of the Archimedean solids, which are convex polyhedra that are composed of two or more types of regular polygons. Specifically, the Great Dodecahedron is a non-convex polyhedron that is made up of 12 faces, which are regular pentagons. It is characterized by its vertex configuration, where each vertex meets five pentagonal faces.
The small cubicuboctahedron is a type of convex polyhedron and is classified as an Archimedean solid. It belongs to the family of polyhedra that are made up of regular polygons, and it features a combination of different types of faces.
The Szilassi polyhedron is an interesting mathematical object that is classified as a toroidal polyhedron. It is notable for being a non-convex, 14-faced polyhedron that has a unique property: each of its faces is a heptagon (7-sided polygon).
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