Search results
Results from the WOW.Com Content Network
A truncated hexagon, t{6}, is a dodecagon, {12}, alternating two types (colors) of edges. An alternated hexagon, h{6}, is an equilateral triangle, {3}. A regular hexagon can be stellated with equilateral triangles on its edges, creating a hexagram. A regular hexagon can be dissected into six equilateral triangles by adding a
The faces are irregular hexagons. Denoting the golden ratio by and putting = +, the hexagons have five equal angles of and one of ().Each face has four long and two short edges.
This includes the 3 regular tiles (triangle, square and hexagon) and 8 irregular ones. [4] Each vertex has edges evenly spaced around it. Three dimensional analogues of the planigons are called stereohedrons. These dual tilings are listed by their face configuration, the number of faces at each vertex of a face.
Hexagonal tilings can be made with the identical {6,3} topology as the regular tiling (3 hexagons around every vertex). With isohedral faces, there are 13 variations. Symmetry given assumes all faces are the same color. Colors here represent the lattice positions. [2] Single-color (1-tile) lattices are parallelogon hexagons.
Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both. This list includes these: all 75 nonprismatic uniform polyhedra; a few representatives of the infinite sets of prisms and antiprisms;
A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices which have 5 triangles. They are the dual of corresponding Goldberg polyhedra, of which all but the smallest one (which is a regular dodecahedron) have mostly hexagonal faces.
For example, a regular hexagon bisects into two type 1 pentagons. Subdivision of convex hexagons is also possible with three (type 3), four (type 4) and nine (type 3) pentagons. By extension of this relation, a plane can be tessellated by a single pentagonal prototile shape in ways that generate hexagonal overlays.
A real life example spherical polyhedron is the football, being a spherical tiling of the truncated Icosahedron. This beach ball would be a hosohedron with 6 spherical lune faces, if the 2 white caps on the ends were removed.