Abstract
Regular polytopes (RPs) are an extension of 2D (two-dimensional) regular polygons and 3D regular polyhedra in n-dimensional ( n ≥ 4 ) space. The high abstraction and perfect symmetry are their most prominent features. The traditional projections only show vertex and edge information. Although such projections can preserve the highest degree of symmetry of the RPs, they can not transmit their metric or topological information. Based on the generalized stereographic projection, this paper establishes visualization methods for 5D RPs, which can preserve symmetries and convey general metric and topological data. It is a general strategy that can be extended to visualize n-dimensional RPs ( n > 5 ).
Highlights
The research of 2D symmetries produces the profound result of planar symmetry groups, which is widely used in the fields of architecture and decoration [4,11,12]
By generalizing the idea of [7], we study in detail the 2D and 3D stereographic projections of 5D
Based on the geometrical meaning of Regular polytopes (RPs), this paper presents a convenient strategy to visualize
Summary
Regular polytopes (RPs) are an extension of 2D regular polygons and 3D regular polyhedra in n-dimensional Euclidean space Rn (n ≥ 4), which have high abstraction and perfect symmetry [1,2,3]. The history of scientific and technological progress shows that the study of symmetry is of great significance [9,10]. It has greatly promoted the integration and development of natural sciences and has a far-reaching impact in practical fields. As a subject closely related to geometry, it is very important to establish the 2D or 3D visualization methods for RPs. Based on the idea of reducing dimensions, many projection methods. Using traditional projections, it is difficult to establish their detailed geometric structure. To this end, in [7], we studied the generalized stereographic projection to observe.
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