The five Platonic solids and their connection to root systems

Oberwolfach'tan

The five Platonic solids and their connection to root systems

Platonic solids have fascinated humans for thousands of years. In ancient times, they were associated with the elements fire, air, water, earth, and aether. These solids are completely symmetrical three-dimensional polyhedra. In this snapshot, it is first explained that there can only be five such polyhedra in the threedimensional space. For this purpose, so-called Schläfli symbols and Coxeter graphs are introduced. More precisely, the (linear) Coxeter graphs correspond to the (linear) Schläfli symbols that, in turn, correspond exactly to the regular convex polyhedra. Through this one-to-one relationship, it is possible to classify the regular convex polytopes in any dimension by exploiting the classification of Coxeter graphs.

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Matematiksel konular

Cebir ve Sayılar Kuramı
Geometri ve Topoloji

Diğer alanlarla ilişkiler

Bilgisayar Bilimeri

Yazar(lar)

Sören Böhm

Lisans

DOI (Dijital nesne belirteci)

10.14760/SNAP-2025-004-EN

PDF indir

snapshot-2025-004.pdf

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Matematiksel konular

Cebir ve Sayılar Kuramı
Analiz
Eğitim ve Eğitim Bilimi
Ayrık Matematik ve Matematiğin Temelleri
Geometri ve Topoloji
Nümerik ve Hesap Analizi
Olasılık Kuramı ve İstatistik

Diğer alanlarla ilişkiler

Kimya ve Yer Bilimler
Bilgisayar Bilimeri
Mühendislik ve Teknoloji
Finans
Beşeri ve Sosyal Bilimler
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Fizik
Matematik Üzerine Düşünceler

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