Lecture

Platonic Solids: Misinterpretations and Correspondences

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

MATH-124: Geometry for architects I

Ce cours entend exposer les fondements de la géométrie à un triple titre : 1/ de technique mathématique essentielle au processus de conception du projet, 2/ d'objet privilégié des logiciels de conception paramétrique 3/ de composante à part entière de l'h ...

Description

This lecture explores the misinterpretations surrounding the five Platonic solids, particularly in relation to Plato's work. It delves into the historical context of the naming of these solids as 'Platonic bodies' and the correspondence between the elements and the polyhedra. The instructor discusses the origins of the regular polyhedra, emphasizing that Plato was a philosopher and not a mathematician. The lecture also touches upon the integration of mathematics into architectural culture, highlighting the importance of rigor in such endeavors. Furthermore, it examines the attempts to integrate the five regular polyhedra into astronomy by Kepler, shedding light on his discoveries regarding the elliptical nature of planetary trajectories.

Instructor

Bernard Cache

Official source

Related concepts (32)

Platonic solid

In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra: Geometers have studied the Platonic solids for thousands of years. They are named for the ancient Greek philosopher Plato who hypothesized in one of his dialogues, the Timaeus, that the classical elements were made of these regular solids.

Semiregular polyhedron

In geometry, the term semiregular polyhedron (or semiregular polytope) is used variously by different authors. In its original definition, it is a polyhedron with regular polygonal faces, and a symmetry group which is transitive on its vertices; today, this is more commonly referred to as a uniform polyhedron (this follows from Thorold Gosset's 1900 definition of the more general semiregular polytope). These polyhedra include: The thirteen Archimedean solids.

Regular skew polyhedron

In geometry, the regular skew polyhedra are generalizations to the set of regular polyhedra which include the possibility of nonplanar faces or vertex figures. Coxeter looked at skew vertex figures which created new 4-dimensional regular polyhedra, and much later Branko Grünbaum looked at regular skew faces. Infinite regular skew polyhedra that span 3-space or higher are called regular skew apeirohedra. According to Coxeter, in 1926 John Flinders Petrie generalized the concept of regular skew polygons (nonplanar polygons) to regular skew polyhedra.

Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johnson solid is the square-based pyramid with equilateral sides (J_1); it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform (i.e., not Platonic solid, Archimedean solid, uniform prism, or uniform antiprism) before they refer to it as a "Johnson solid".

Archimedean solid

In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed of only one type of polygon), excluding the prisms and antiprisms, and excluding the pseudorhombicuboctahedron. They are a subset of the Johnson solids, whose regular polygonal faces do not need to meet in identical vertices.

Related lectures (54)

Geometry: Course Overview & 5 Regular Polyhedra

Explores geometry basics, 5 regular polyhedra construction, and their link to ancient physics and planets.

Regular Polyhedra: Symmetries & Generation

Explores the properties of regular polyhedra, their symmetries, generation, and historical misconceptions.

Symmetries of Regular Polyhedra

Explores the historical background and significance of symmetries in regular polyhedra, shedding new light on Euclid's Elements.

Regular Polyhedra: Definitions and Symmetries

Explores the definitions and symmetries of regular polyhedra, shedding light on ancient geometry and modern mathematical formalization.

Limitation to 5 Polyhedra