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...

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...

In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-)  'many' and ἕδρον (-hedron)  'base, seat') is a three-dimensional figure...

object is called a torus. The term toroid is also used to describe a toroidal polyhedron. In this context a toroid need not be circular and may have any...

spherical polyhedra – tessellations of the sphere – and toroidal polyhedra – tessellations of the toroids. Projective polyhedra are also referred to as elliptic...

geometry, the Császár polyhedron (Hungarian: [ˈt͡ʃaːsaːr]) is a nonconvex toroidal polyhedron with 14 triangular faces. This polyhedron has no diagonals;...

Look up toroidal in Wiktionary, the free dictionary. Toroidal describes something which resembles or relates to a torus or toroid: Toroidal coordinates...

Spherical geometry Spherical trigonometry Polyhedron Projective polyhedron Toroidal polyhedron Conway polyhedron notation Sarhangi, Reza (September 2008)...

the number of holes. The term "toroidal polyhedron" is also used for higher-genus polyhedra and for immersions of toroidal polyhedra. The homeomorphism...

Szilassi at the Mathematics Genealogy Project On some regular toroids, Lajos Szilassi Szilassi polyhedron, toroidal polyhedron publications, Lajos Szilassi...

Goldberg polyhedron Kepler-Poinsot polyhedron List of regular polytopes Prince Rupert's cube Regular polytope Regular skew polyhedron Toroidal polyhedron Gardner...

between inner pentagons and outer decagons. The remaining part is a toroidal polyhedron. The truncated icosidodecahedron has seven special orthogonal projections...

tilings of other elliptic, flat or toroidal (p−1)-surfaces – see elliptic tiling and toroidal polyhedron. A polyhedron is understood as a surface whose...

on Hamiltonian cycles in 4-vertex-connected toroidal graphs Topological graph theory Toroidal polyhedron Orbanić et al. (2004). Marušič & Pisanski (2000)...

{\displaystyle \chi =2} , so for a convex polyhedron the sum of the defects is 4 π {\displaystyle 4\pi } , while a toroidal polyhedron has χ = 0 {\displaystyle \chi...

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...

of a genus 5 toroidal is −4, like this Stewart toroid: v=72, e=168, f=88. Arthur Cayley used density as a way to modify Euler's polyhedron formula (V −...

rhombic dodecahedron. The excavated truncated rhombicuboctahedron is a toroidal polyhedron, constructed from a truncated rhombicuboctahedron with its 12 irregular...

given polyhedron. Any convex polyhedron's surface has an Euler characteristic. This equation, stated by Euler in 1758, is known as Euler's polyhedron formula...

prism is topologically identical to an n-gonal prism. A toroidal prism is a nonconvex polyhedron like a crossed prism, but without bottom and top base faces...

Euler characteristic suggests, the small cubicuboctahedron is a toroidal polyhedron of genus 3 (topologically it is a surface of genus 3), and thus can...

of volumes of various solids, including pyramids, prisms (and other polyhedrons), cubes, cylinders, cones (and truncated cones). The Pythagoreans dealt...

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...

the octahemioctahedron or allelotetratetrahedron is a nonconvex uniform polyhedron, indexed as U3. It has 12 faces (8 triangles and 4 hexagons), 24 edges...

square faces (augmented), with their common surfaces removed. A toroidal polyhedron can also be defined connecting a holed-face to a holed-faced on the...

triangular prism. Császár polyhedron – Toroidal polyhedron with 14 triangle faces Steffen's polyhedron – Flexible polyhedron with 14 triangle faces Sloane...

generally regular toroidal polyhedra {p,q}b,c can be defined if either p or q are even, although only euclidean ones above can exist as toroidal polyhedra in...

A noble polyhedron is one which is isohedral (all faces the same) and isogonal (all vertices the same). They were first studied in any depth by Edmund...

uniform prisms, has 14 faces. The Szilassi polyhedron and its dual, the Császár polyhedron, are the simplest toroidal polyhedra; they have 14 vertices and 14...

triacontahedron and the 30 rhombic prisms are removed, you can create a toroidal polyhedron with all regular polygon faces. Rhombicosidodecahedron (expanded...