A polyhedral torus can be constructed to approximate a torus surface, from a net of quadrilateral faces, like this 6x4 example.
In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus (g) of 1 or greater. Notable examples include the Császár and Szilassi polyhedra.
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In geometry, a toroidalpolyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus (g) of 1 or greater. Notable examples...
object is called a torus. The term toroid is also used to describe a toroidalpolyhedron. In this context a toroid need not be circular and may have any...
In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many', and ἕδρον (-hedron) 'base, seat') is a three-dimensional shape...
of the theorem states that all toroidal subdivisions can be colored with seven or fewer colors. The Szilassi polyhedron has an axis of 180-degree symmetry...
the number of holes. The term "toroidalpolyhedron" is also used for higher-genus polyhedra and for immersions of toroidal polyhedra. The homeomorphism...
Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical...
between inner pentagons and outer decagons. The remaining part is a toroidalpolyhedron. The truncated icosidodecahedron has seven special orthogonal projections...
vertex of a polyhedron; the defect of a hyperbolic triangle; and the excess also arises in two ways: the excess of a toroidalpolyhedron. the excess of...
dimensions as the Szilassi polyhedron, the simplest toroidalpolyhedron alongside its dual with 7 vertices, the Császár polyhedron. In three-dimensional space...
tilings of other elliptic, flat or toroidal (p−1)-surfaces – see elliptic tiling and toroidalpolyhedron. A polyhedron is understood as a surface whose...
diminishment, or dissection. Near-miss Johnson solid Catalan solid Toroidalpolyhedron Johnson, Norman W. (1966). "Convex Solids with Regular Faces". Canadian...
of volumes of various solids, including pyramids, prisms (and other polyhedrons), cubes, cylinders, cones (and truncated cones). The Pythagoreans dealt...
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive...
Szilassi at the Mathematics Genealogy Project On some regular toroids, Lajos Szilassi Szilassi polyhedron, toroidalpolyhedron publications, Lajos Szilassi...
spherical polyhedra – tessellations of the sphere – and toroidal polyhedra – tessellations of the toroids. Projective polyhedra are also referred to as elliptic...
Euler characteristic suggests, the small cubicuboctahedron is a toroidalpolyhedron of genus 3 (topologically it is a surface of genus 3), and thus can...
ladders are toroidal. More generally, any graph with crossing number 1 is toroidal. Some graphs with greater crossing numbers are also toroidal: the Möbius–Kantor...
rhombic dodecahedron. The excavated truncated rhombicuboctahedron is a toroidalpolyhedron, constructed from a truncated rhombicuboctahedron with its 12 irregular...
square faces (augmented), with their common surfaces removed. A toroidalpolyhedron can also be defined connecting a holed-face to a holed-faced on the...
on. One particularly interesting example is the Szilassi polyhedron, a Toroidalpolyhedron with 7 non-convex six sided faces. Frank Chester. "The Geometry...
numbers of vertices (corners), edges and faces in the given polyhedron. Any convex polyhedron's surface has Euler characteristic χ = V − E + F = 2 ....
triacontahedron and the 30 rhombic prisms are removed, you can create a toroidalpolyhedron with all regular polygon faces. Rhombicosidodecahedron (expanded...
Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified...
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