Triakis triangular tiling
Encyclopedia
In geometry
, the Triakis triangular tiling is a tiling of the Euclidean plane. It is an equilateral triangular tiling with each triangle divided into three obtuse triangles (angles 30-30-120) from the center point.
Conway
calls it a kisdeltile, constructed as a kis operation applied to a triangular tiling (deltille).
It is labeled V3.12.12 because each isosceles triangle face has two types of vertices: one with 3 triangles, and two with 12 triangles.
which has one triangle and two dodecagons at each vertex.
figures have (*n32) reflectional symmetry.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the Triakis triangular tiling is a tiling of the Euclidean plane. It is an equilateral triangular tiling with each triangle divided into three obtuse triangles (angles 30-30-120) from the center point.
Conway
John Horton Conway
John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
calls it a kisdeltile, constructed as a kis operation applied to a triangular tiling (deltille).
It is labeled V3.12.12 because each isosceles triangle face has two types of vertices: one with 3 triangles, and two with 12 triangles.
Dual tiling
It is the dual tessellation of the truncated hexagonal tilingTruncated hexagonal tiling
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane. There are 2 dodecagons and one triangle on each vertex....
which has one triangle and two dodecagons at each vertex.
Related polyhedra and tilings
It is topologically related to a sequence of polyhedra and continue into tilings of the hyperbolic plane. These vertex-transitiveVertex-transitive
In geometry, a polytope is isogonal or vertex-transitive if, loosely speaking, all its vertices are the same...
figures have (*n32) reflectional symmetry.
 V3.6.6 Triakis tetrahedron In geometry, a triakis tetrahedron is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated tetrahedron.It can be seen as a tetrahedron with triangular pyramids added to each face; that is, it is the Kleetope of the tetrahedron... (*332) |
 V3.8.8 Triakis octahedron In geometry, a triakis octahedron is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated cube.It can be seen as an octahedron with triangular pyramids added to each face; that is, it is the Kleetope of the octahedron. It is also sometimes called a trisoctahedron, or, more... (*432) |
 V3.10.10 Triakis icosahedron In geometry, the triakis icosahedron is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated dodecahedron.It can be seen as an icosahedron with triangular pyramids augmented to each face; that is, it is the Kleetope of the icosahedron... (*532) |
 V3.12.12 (*632) |
 V3.14.14 (*732) |