Aesthetic Patterns with Symmetries of the Regular Polyhedron
نویسندگان
چکیده
A fast algorithm is established to transform points of the unit sphere into fundamental region symmetrically. With the resulting algorithm, a flexible form of invariant mappings is achieved to generate aesthetic patterns with symmetries of the regular polyhedra.
منابع مشابه
Highly Symmetric and Congruently Tiled Meshes for Shells and Domes
We describe the generation of all possible shell and dome shapes that can be uniquely meshed (tiled) using a single type of mesh face (tile), and following a single meshing (tiling) rule that governs the mesh (tile) arrangement with maximal vertex, edge and face symmetries. Such tiling arrangements or congruently tiled meshed shapes, are frequently found in chemical forms (fullerenes or Bucky b...
متن کاملHierarchical Modular Systems with Elements of Folk Art
Hierarchical modular systems are composed of identical elements assembled by systematic rules based on rotational group. The systems are characterized by hierarchical symmetries and their regular outlines defined by the last rules. To introduce fundamental an element of Japanese folk art into an initial module of our system, we can form various hierarchical symmetric patterns composed of identi...
متن کاملPatterns on Triply Periodic Polyhedra
This paper discusses patterns on triply periodic polyhedra, infinite polyhedra that repeat in three independent directions in Euclidean 3-space. We further require that all the vertices be congruent by a symmetry of the polyhedron, i.e. that they be uniform, and also that each of the faces is a single regular polygon. We believe that we are the first to apply patterns to such polyhedra. The pat...
متن کاملCalculations of Dihedral Groups Using Circular Indexation
In this work, a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$. Each element of the sequence represents a vertex of the polygon. Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis. Here each symmetry is considered as a system that takes an input circular sequence and g...
متن کاملThe small step toward asymmetry: Aesthetic judgment of broken symmetries
Symmetry and complexity both affect the aesthetic judgment of abstract patterns. However, although beauty tends to be associated with symmetry, there are indications that small asymmetries can also be beautiful. We investigated the influence of small deviations from symmetry on people's aesthetic liking for abstract patterns. Breaking symmetry not only decreased patterns' symmetry but also incr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Symmetry
دوره 9 شماره
صفحات -
تاریخ انتشار 2017