In this paper we present a simple proof of the classification theorem of Archimedean solids (known as Keplero’s theorem), which is based on the concept of Euler characteristic. It extends the classical proof of the classification theorem of Platonic solids. Then we describe simple geometric constructions to obtain all Archimedean solids starting from Platonic ones. A discussion on Johnson solids completes the paper. The proposed techniques and methods are very elementary and can be included in different topics studied by high school students.
SOLIDI PLATONICI e ARCHIMEDEI: classificazione e costruzioni geometriche. Una proposta didattica basata sulla caratteristica di Eulero / Cavicchioli, Alberto; Prandini, Monica. - In: L'INSEGNAMENTO DELLA MATEMATICA E DELLE SCIENZE INTEGRATE. - ISSN 1123-7570. - ELETTRONICO. - 39B n. 1:(2016), pp. 19-51.
SOLIDI PLATONICI e ARCHIMEDEI: classificazione e costruzioni geometriche. Una proposta didattica basata sulla caratteristica di Eulero.
CAVICCHIOLI, Alberto;
2016
Abstract
In this paper we present a simple proof of the classification theorem of Archimedean solids (known as Keplero’s theorem), which is based on the concept of Euler characteristic. It extends the classical proof of the classification theorem of Platonic solids. Then we describe simple geometric constructions to obtain all Archimedean solids starting from Platonic ones. A discussion on Johnson solids completes the paper. The proposed techniques and methods are very elementary and can be included in different topics studied by high school students.
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