The 15th monohedral convex pentagonal type, discovered in 2015
In geometry, a pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon.
A regular pentagonal tiling on the Euclidean plane is impossible because the internal angle of a regular pentagon, 108°, is not a divisor of 360°, the angle measure of a whole turn. However, regular pentagons can tile the hyperbolic plane with four pentagons around each vertex (or more) and sphere with three pentagons; the latter produces a tiling that is topologically equivalent to the dodecahedron.[1]
^Chung, Ping Ngai; Fernandez, Miguel A.; Li, Yifei; Mara, Michael; Morgan, Frank; Plata, Isamar Rosa; Shah, Nirlee; Vieira, Luis Sordo; Wikner, Elena (2012-05-01), "Isoperimetric Pentagonal Tilings", Notices of the American Mathematical Society, 59 (5): 632, doi:10.1090/noti838, ISSN 0002-9920
geometry, a pentagonaltiling is a tiling of the plane where each individual piece is in the shape of a pentagon. A regular pentagonaltiling on the Euclidean...
particular form of the tiling, dual to the snub square tiling, has tiles with the minimum possible perimeter among all pentagonaltilings. Another, overlaying...
Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is...
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...
regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at...
American amateur mathematician most famous for her discoveries of pentagonaltilings in geometry. Rice was born February 16, 1923, in St. Petersburg, Florida...
wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form...
echinoderms with a pentagonal shape. A Ho-Mg-Zn icosahedral quasicrystal formed as a pentagonal dodecahedron. The faces are true regular pentagons. A pyritohedral...
quotient space of the hyperbolic order-4 pentagonaltiling, by distorting the pentagrams back into regular pentagons. As such, it is topologically a regular...
called bihedra, flat polyhedra, or doubly covered polygons. As a spherical tiling, a dihedron can exist as nondegenerate form, with two n-sided faces covering...
composed of 12 pentagonal faces (six pairs of parallel pentagons), intersecting each other making a pentagrammic path, with five pentagons meeting at each...
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex...
triangles: The dual tiling is called an order-7-3 floret pentagonaltiling, and is related to the floret pentagonaltiling. This semiregular tiling is a member...
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