Pentagon-based radial tiling with triangles and rectangles and its spatial interpretation
Apstrakt
The paper considers a type of radial pentagon-based tiling consisted of two shapes: triangle
and rectangle. The obtained solution has a spatial interpretation in a 3D arrangement of
equilateral triangles and squares dictated by the particular array of concave cupolae of the
second sort, minor type (CC-II-5.m). These cupolae are arranged so that their decagonal
bases partly overlap, making a pentagonal pattern (similar to one of the Penrose tiling).
Covering the folds between the faces of such a polyhedral structure with polygons,we use
exactly equilateral triangles and squares, thanks to the trigonometric properties of CC-II-5.m.
Observed in the orthogonal projection onto the plane of the polygonal bases, this 3D “covering” is viewed as a pentagonal-based radial tiling in the Euclidean plane. Equilateral triangles
will be projected into congruent isosceles triangles corresponding to those obtained by the
radial section of a regular pentagon in 5 parts. The squares are projecte...d into rectangles
whose ratio a:b = 1:φ/√(1+φ2), where φ is the golden ratio. These triangles and rectangles
form a radial tiling consisting of 5 sectors of the plane, where the established tiles’ patterns
are repeated locally periodically. However, with 5-fold rotation of the pattern, the tilling itself
is non-periodic. The various tiling solution that can be obtained in this way may serve as
inspiration for the geometric design, especially interesting in architecture and applied arts,
e.g. for rosettes, brise soleils, mosaics, stained glass, fences, partition screens and the like
Ključne reči:
tiling / tile / pentagon / 5-fold symmetry / triangle / rectangleIzvor:
SmartArt | Књига апстраката| Book of Abstracts, 2021, 58-Izdavač:
- Faculty of Applied Arts, University of Arts in Belgrade, Serbia
Finansiranje / projekti:
Napomena:
- https://smartart-conference.rs/book-of-abstracts/