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...

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...

which resembles a torus Toroidal polyhedron Toroidal coordinates, a three-dimensional orthogonal coordinate system Toroidal and poloidal coordinates...

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

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

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

Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical...

cube#Generalizations Quasicrystal Regular polyhedron Semiregular polyhedron Toroidal polyhedron Uniform polyhedron Steckles, Katie. "The Unwanted Shape"....

dimensions as the Szilassi polyhedron, the simplest toroidal polyhedron alongside its dual with 7 vertices, the Császár polyhedron. In three-dimensional space...

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

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

vertex of a polyhedron; the defect of a hyperbolic triangle; and the excess also arises in two ways: the excess of a toroidal polyhedron. the excess of...

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 −...

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

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

diminishment, or dissection. Near-miss Johnson solid Catalan solid Toroidal polyhedron Johnson, Norman W. (1966). "Convex Solids with Regular Faces". Canadian...

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

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...

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...

on. One particularly interesting example is the Szilassi polyhedron, a Toroidal polyhedron with 7 non-convex six sided faces. Frank Chester. "The Geometry...

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

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...

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...

numbers of vertices (corners), edges and faces in the given polyhedron. Any convex polyhedron's surface has Euler characteristic   χ = V − E + F = 2   ....

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...

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

rhombic prisms are removed, you can create a toroidal polyhedron with all regular polygon faces. This toroid has 86 faces (8 triangles and 78 squares),...