A new class of monohedral pentagonal spherical tilings with GeoGebra
نویسندگان
چکیده
منابع مشابه
Infinite families of monohedral disk tilings
A tiling of a planar shape is called monohedral if all tiles are congruent to each other. We will investigate the possibility of producing monohedral tilings of the disk. Such tilings are produced on a daily basis by pizza chefs by taking radial cuts distributed evenly around the centre of the pizza. After constructing this tiling, a neighbourhood of the origin has non-trivial intersection with...
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Some tiles derived from regular polygons can produce spiral tilings of the plane [1]. This paper considers some more general classes of tilings with tiles derived from regular polygons, some have central symmetry, many have periodic symmetry, some have both, and a few have no symmetry at all. Any of these tiling patterns could be the basis for some interesting mathematical art, for example by c...
متن کاملProperties of Nodes in Pentagonal Tilings
A node of valence k in an edge-to-edge tiling is a point that is the common vertex of k tiles. We show that an edge-to-edge tiling of plane by pentagons each of which has m nodes of valence 3 and 5 − m nodes of valence k has properties of (m, k) = (3, 4) or (m, k) = (4, 6) if it is normal. Then we discuss tilings by congruent convex pentagons using the properties.
متن کاملSystematic Study of Convex Pentagonal Tilings, II: Tilings by Convex Pentagons with Four Equal-length Edges
We derived 14 types of tiling cases under a restricted condition in our previous report, which studied plane tilings with congruent convex pentagons. That condition is referred to as the category of the simplest set of node (vertex of edge-to-edge tiling) conditions when the tile is a convex pentagon with four equal-length edges. This paper shows the detailed properties of convex pentagonal til...
متن کاملRibbon Tilings From Spherical Ones
The problem of classifying all tile-k-transitive tilings of the innnite 2-dimensional ribbon (and pinched-ribbon) is shown to be solvable by classifying certain tile-k-transitive tilings of the sphere, for all k 2 N. Complete results are listed for k 3.
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ژورنال
عنوان ژورنال: Portugaliae Mathematica
سال: 2018
ISSN: 0032-5155
DOI: 10.4171/pm/2006