Triheptagonal tiling
Encyclopedia
In geometry
, the triheptagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified
Order-3 heptagonal tiling. There are two triangle
s and two heptagons alternating on each vertex
. It has Schläfli symbol of t1{7,3}.
Compare to trihexagonal tiling
with vertex configuration
3.6.3.6.
polyhedra with vertex figure
(3.n.3.n) and (*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 triheptagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified
Rectification (geometry)
In Euclidean geometry, rectification is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points...
Order-3 heptagonal tiling. There are two triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
s and two heptagons alternating on each vertex
Vertex (geometry)
In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...
. It has Schläfli symbol of t1{7,3}.
Compare to trihexagonal tiling
Trihexagonal tiling
In geometry, the trihexagonal tiling is a semiregular tiling of the Euclidean plane. There are two triangles and two hexagons alternating on each vertex...
with vertex configuration
Vertex configuration
In geometry, a vertex configuration is a short-hand notation for representing the vertex figure of a polyhedron or tiling as the sequence of faces around a vertex. For uniform polyhedra there is only one vertex type and therefore the vertex configuration fully defines the polyhedron...
3.6.3.6.
Images
 Klein disk model of this tiling preserves straight lines, but distorts angles |
 The dual tiling is called an Order-7-3 rhombille tiling, made from rhombic faces, alternating 3 and 7 per vertex. |
Related polyhedra and tilings
This tiling is topologically part of sequence of rectifiedRectification (geometry)
In Euclidean geometry, rectification is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points...
polyhedra with vertex figure
Vertex figure
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
(3.n.3.n) and (*n32) reflectional symmetry.
 (3.3.3.3) Octahedron In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.... (*332) and (*432) |
 (3.4.3.4) Cuboctahedron In geometry, a cuboctahedron is a polyhedron with eight triangular faces and six square faces. A cuboctahedron has 12 identical vertices, with two triangles and two squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such it is a quasiregular polyhedron,... (*432) |
 (3.5.3.5) Icosidodecahedron In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon... (*532) |
 (3.6.3.6) (*632) |
 (3.7.3.7) (*732) |
 (3.8.3.8) (*832) |
See also
- Trihexagonal tilingTrihexagonal tilingIn geometry, the trihexagonal tiling is a semiregular tiling of the Euclidean plane. There are two triangles and two hexagons alternating on each vertex...
- 3.6.3.6 tiling- Rhombille tiling - dual V3.6.3.6 tiling
- Tilings of regular polygons
- List of uniform tilings