In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general...

In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting...

Cauchy in 1812 that there are only four regular star polyhedrons, known as the Kepler–Poinsot polyhedron. Brückner (1900) extended the stellation theory...

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. They may be obtained by stellating the regular convex dodecahedron and...

dirhombidodecahedron, also called Skilling's figure, is a degenerate uniform star polyhedron. It was proven in 1970 that there are only 75 uniform polyhedra other...

antiprisms, the convex polyhedrons as in 5 Platonic solids and 13 Archimedean solids—2 quasiregular and 11 semiregular— the non-convex star polyhedra as in 4...

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

In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal (from Greek τόξον  'arc') or edge-transitive if its symmetries...

star Pentagramma mirificum Regular star 4-polytope Rub el Hizb Star (glyph) Star polyhedron, Kepler–Poinsot polyhedron, and uniform star polyhedron Starfish...

geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4. It has 7 faces (4 triangles and 3 squares), 12 edges...

In geometry, the density of a star polyhedron is a generalization of the concept of winding number from two dimensions to higher dimensions, representing...

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...

In geometry, the excavated dodecahedron is a star polyhedron that looks like a dodecahedron with concave pentagonal pyramids in place of its faces. Its...

In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces (8 triangles, 6 squares, and 6 octagons), 48 edges...

uniform star polyhedron some of whose faces pass through its center. These "hemi" faces lie parallel to the faces of some other symmetrical polyhedron, and...

an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices...

In geometry, the small triambic icosahedron is a star polyhedron composed of 20 intersecting non-regular hexagon faces. It has 60 edges and 32 vertices...

geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12 pentagrams...

Coxeter diagram . Nonconvex great rhombicuboctahedron - a uniform star polyhedron, with Schläfli symbol r{4,3/2}, and Coxeter diagram . This disambiguation...

uniform star polyhedron with Wythoff symbol of the form 3 | p q or ⁠3/2⁠ | p q are ditrigonal, at least if p and q are not 2. Each polyhedron includes...

faces of a polyhedron are all faces in this more general sense. In elementary geometry, a face is a polygon on the boundary of a polyhedron. (Here a "polygon"...

uniformity when changing a spherical polyhedron to its planar counterpart can push faces through the centre of the polyhedron and back out the other side, changing...

square, inverted as {4/3}, is an octagram, t{4/3}={8/3}. The uniform star polyhedron stellated truncated hexahedron, t'{4,3}=t{4/3,3} has octagram faces...

solids and (star) Kepler–Poinsot polyhedra – form dual pairs, where the regular tetrahedron is self-dual. The dual of an isogonal polyhedron (one in which...

forms. Platonic solid Kepler-Poinsot polyhedra — regular star polyhedron Star polygon — regular star polygons 4-polytope 5-polytope 6-polytope Coxeter 1973...

geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U67. It has 62 faces (20 triangles, 30 squares and 12 pentagrams)...

dodecadodecahedron (or stellatruncated dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U59. It is given a Schläfli symbol t0,1,2{5⁄3,5}. It has 54...

icosidodecahedron is a degenerate uniform star polyhedron. Its edges are doubled, making it degenerate. The star has 32 faces (20 triangles and 12 pentagons)...

dirhombicosidodecahedron (or great snub disicosidisdodecahedron) is a nonconvex uniform polyhedron, indexed last as U75. It has 124 faces (40 triangles, 60 squares, and...

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...