Pavage triangulaire allongéIn geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. It is named as a triangular tiling elongated by rows of squares, and given Schläfli symbol {3,6}:e. Conway calls it a isosnub quadrille. There are 3 regular and 8 semiregular tilings in the plane. This tiling is similar to the snub square tiling which also has 3 triangles and two squares on a vertex, but in a different order.
Apeirogonal antiprismIn geometry, an apeirogonal antiprism or infinite antiprism is the arithmetic limit of the family of antiprisms; it can be considered an infinite polyhedron or a tiling of the plane. If the sides are equilateral triangles, it is a uniform tiling. In general, it can have two sets of alternating congruent isosceles triangles, surrounded by two half-planes. The apeirogonal antiprism is the arithmetic limit of the family of antiprisms sr{2, p} or p.3.3.3, as p tends to infinity, thereby turning the antiprism into a Euclidean tiling.
Coloration uniformelien=//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Square_tiling_uniform_colorings.png/240px-Square_tiling_uniform_colorings.png|vignette|240x240px| Le pavage carré possède 9 colorations uniformes :1111, 1112(a), 1112(b),1122, 1123(a), 1123(b),1212, 1213, 1234. En géométrie, une coloration uniforme est une propriété d'une figure uniforme ( pavage uniforme (en) ou polyèdre uniforme ) qui est colorée pour être isogonale. Différentes symétries peuvent être présentes sur une figure géométrique ayant des faces colorées suivant différents motifs uniformes de couleurs.
Rhombille tilingIn geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles, and sets of six rhombi meet at their 60° angles. The rhombille tiling can be seen as a subdivision of a hexagonal tiling with each hexagon divided into three rhombi meeting at the center point of the hexagon.
Uniform polytopeIn geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets. The uniform polytopes in two dimensions are the regular polygons (the definition is different in 2 dimensions to exclude vertex-transitive even-sided polygons that alternate two different lengths of edges). This is a generalization of the older category of semiregular polytopes, but also includes the regular polytopes. Further, star regular faces and vertex figures (star polygons) are allowed, which greatly expand the possible solutions.
Construction de WythoffEn géométrie, une construction de Wythoff, nommée en l'honneur du mathématicien Willem Abraham Wythoff, est une méthode pour construire un polyèdre uniforme ou un pavage plan. On l'appelle souvent construction kaléidoscopique de Wythoff. Elle repose sur le pavage d'une sphère, avec des triangles sphériques. Si trois miroirs sont placés de telle manière que leurs plans se coupent en un point unique, alors les miroirs entourent un triangle sphérique sur la surface d'une sphère quelconque centrée en ce point et par réflexions répétées, on obtient une multitude de copies du triangle.
Triheptagonal tilingIn geometry, the triheptagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified Order-3 heptagonal tiling. There are two triangles and two heptagons alternating on each vertex. It has Schläfli symbol of r{7,3}. Compare to trihexagonal tiling with vertex configuration 3.6.3.6. In geometry, the 7-3 rhombille tiling is a tessellation of identical rhombi on the hyperbolic plane. Sets of three and seven rhombi meet two classes of vertices.
Trioctagonal tilingIn geometry, the trioctagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified Order-3 octagonal tiling. There are two triangles and two octagons alternating on each vertex. It has Schläfli symbol of r{8,3}. From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular octagonal tiling. Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms. It c
Pavage hexagonalLe pavage hexagonal est, en géométrie, un pavage du plan euclidien constitué d'hexagones réguliers. C'est l'un des trois pavages réguliers du plan euclidien, avec le pavage carré et le pavage triangulaire. Le pavage hexagonal possède un symbole de Schläfli de {6,3}, signifiant que chaque sommet est entouré par 3 hexagones. Le Théorème du nid d'abeille énonce que le pavage hexagonal régulier est la partition du plan en surfaces égales ayant le plus petit périmètre.
Pavage triangulaireIn geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons. Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees. The triangular tiling has Schläfli symbol of {3,6}. English mathematician John Conway called it a deltille, named from the triangular shape of the Greek letter delta (Δ).
