Edge-to-Edge Tilings with Vertex, Edge and Tile Transivity Properties

Edge-to-edge tilings with vertex, edge and tile transitivity properties An (a, b, c) tiling T is an a-isogonal, b-isotoxal and c-isohedral tiling, that is, T forms, respectively, a orbits of vertices, b orbits of edges and c orbits of tiles under its symmetry group. This study gives a method of...

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Main Author: Tomenes, Mark
Format: text
Published: Archīum Ateneo 2021
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Online Access:https://archium.ateneo.edu/theses-dissertations/539
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Institution: Ateneo De Manila University
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spelling ph-ateneo-arc.theses-dissertations-16652021-10-06T05:00:04Z Edge-to-Edge Tilings with Vertex, Edge and Tile Transivity Properties Tomenes, Mark Edge-to-edge tilings with vertex, edge and tile transitivity properties An (a, b, c) tiling T is an a-isogonal, b-isotoxal and c-isohedral tiling, that is, T forms, respectively, a orbits of vertices, b orbits of edges and c orbits of tiles under its symmetry group. This study gives a method of constructing an (a, b, c) tiling of the Euclidean (E 2 ), hyperbolic (H2 ) or spherical (S 2 ) plane. The method allows for a complete enumeration of the (a, 2, c) tilings of E 2 and S 2 as well as a listing of (a, 3, c) tilings of E 2 derived from tilings by regular polygons, which will be presented. Moreover, classes of (1 , b, c) tilings of E 2 , H2 and S 2 will be shown, particularly those derived from [p n ] tilings. 2021-01-01T08:00:00Z text https://archium.ateneo.edu/theses-dissertations/539 Theses and Dissertations (All) Archīum Ateneo (a, b, c) tiling, a-isogonal, b-isotoxal, c-isohedral
institution Ateneo De Manila University
building Ateneo De Manila University Library
continent Asia
country Philippines
Philippines
content_provider Ateneo De Manila University Library
collection archium.Ateneo Institutional Repository
topic (a, b, c) tiling, a-isogonal, b-isotoxal, c-isohedral
spellingShingle (a, b, c) tiling, a-isogonal, b-isotoxal, c-isohedral
Tomenes, Mark
Edge-to-Edge Tilings with Vertex, Edge and Tile Transivity Properties
description Edge-to-edge tilings with vertex, edge and tile transitivity properties An (a, b, c) tiling T is an a-isogonal, b-isotoxal and c-isohedral tiling, that is, T forms, respectively, a orbits of vertices, b orbits of edges and c orbits of tiles under its symmetry group. This study gives a method of constructing an (a, b, c) tiling of the Euclidean (E 2 ), hyperbolic (H2 ) or spherical (S 2 ) plane. The method allows for a complete enumeration of the (a, 2, c) tilings of E 2 and S 2 as well as a listing of (a, 3, c) tilings of E 2 derived from tilings by regular polygons, which will be presented. Moreover, classes of (1 , b, c) tilings of E 2 , H2 and S 2 will be shown, particularly those derived from [p n ] tilings.
format text
author Tomenes, Mark
author_facet Tomenes, Mark
author_sort Tomenes, Mark
title Edge-to-Edge Tilings with Vertex, Edge and Tile Transivity Properties
title_short Edge-to-Edge Tilings with Vertex, Edge and Tile Transivity Properties
title_full Edge-to-Edge Tilings with Vertex, Edge and Tile Transivity Properties
title_fullStr Edge-to-Edge Tilings with Vertex, Edge and Tile Transivity Properties
title_full_unstemmed Edge-to-Edge Tilings with Vertex, Edge and Tile Transivity Properties
title_sort edge-to-edge tilings with vertex, edge and tile transivity properties
publisher Archīum Ateneo
publishDate 2021
url https://archium.ateneo.edu/theses-dissertations/539
_version_ 1728621335199875072