Four-dimensional convex, regular polytopes

Kamps, Su-Elle (2020) Four-dimensional convex, regular polytopes. Bachelor's Thesis, Mathematics.

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Abstract

Since Ancient times, Mathematicians have been interested in the study of convex, regular polyhedra and their beautiful symmetries. These five polyhedra are also known as the Platonic Solids. In the 19th century, the four-dimensional analogues of the Platonic solids were described mathematically, adding one regular polytope to the collection with no analogue regular polyhedron. This thesis describes the six convex, regular polytopes in four-dimensional Euclidean space. The focus lies on deriving information about their cells, faces, edges and vertices. Besides that, the symmetry groups of the polytopes are touched upon. To better understand the notions of regularity and symmetry in four dimensions, our journey begins in three-dimensional space. In this light, the thesis also works out the details of a proof of prof. dr. J. Top, showing there exist exactly five convex, regular polyhedra in three-dimensional space.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Top, J. and Kilicer, P.
Degree programme:	Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	05 Jan 2021 12:00
Last Modified:	05 Jan 2021 12:00
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/23765

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