Oktaedrske mnogoterosti : delo diplomskega seminarja

Šipec, Katarina (author), Strle, Sašo (mentor)

V tem delu predstavimo mnogoterosti, ki jih lahko dobimo s štirimi lepljenji po dveh lic oktaedra. Ker nastali takšni zlepki niso vedno mnogoterosti, vpeljemo pojem prisekanega oktaedra in obravnavamo lepljenja njegovih šestkotnih lic. Najprej se osredotočimo na analogna lepljenja mnogokotnikov v kompaktne sklenjene ploskve. Nastale mnogoterosti iz prisekanega oktaedra ločimo glede na njihov rob in za vsak rob zabeležimo eno lepljenje v mnogoterost z izbranim robom.

• Language: Slovenian
• Keywords: oktaeder, mnogoterost, lepljenje, homeomorfizem, rob, kvocientni prostor, orientacija, ploskev
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-128910
• UDC: 515.1
• COBISS.SI-ID: 73955075
• Publication date in RUL: 15.08.2021

Secondary language

• Language: English
• Title: Octahedral manifolds

Abstract

In this work, we present the manifolds that can be obtained by gluing together in pairs the faces of an octahedron. Since the resulting gluings are not always manifolds, we introduce the notion of a truncated octahedron and consider the gluings of its hexagonal faces. We first focus on analogous gluings of polygons into compact surfaces without boundary. The resulting manifolds obtained from the truncated octahedron are separated according to their boundary, and for each boundary we present one gluing into the manifold with the selected boundary.

• Keywords: octahedron, manifold, gluing, homeomorphism, boundary, quotient space, orientation, surface