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Lecture

Crystal Symmetry: Axial Classes and Platonic Solids

In course

MSE-100: Introduction to materials science

This course relates the structural elements of materials to their mechanical, thermal, electric, magnetic, and optical properties. Hands-on laboratories and team projects offer insight into the profession of materials engineers. ...

Description

This lecture introduces the symmetry of crystals, focusing on the seven types of axial crystal classes and their international symbols. It also covers the five Platonic solids and the stereographic projection used to image space groups.

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Instructors (2)

Francesco Stellacci

Francesco Stellacci graduated in Materials Engineering at the Politecnico di Milano in 1998 with a thesis on photochromic polymers with Prof. Giuseppe Zerbi and Mariacarla Gallazzi. In 1999 he moved to the Chemistry Department of the University of Arizona for as a post-doc in the group of Joe Perry in close collaboration with the group of Seth Marder. In 2002 he moved to the Department of Materials Science and Engineering at the Massachusetts Institute of Technology as an assistant professor. He was then promoted to associate without (2006) and with tenure (2009). In 2010 he moved to the Institute of Materials at EPFL as a full Professor. He holds the Alcan EP Chair. Francesco was one of the recipients of the Technology Review TR35 "35 Innovator under 35" award in 2005, and the Popular Science Magazine "Brilliant 10" award in 2007. He has been a Packard Fellow starting 2005.

Pierre-Etienne Bourban

Background 1990 Ingénieur en science des matériaux 1993 PhD in materials science Activities 1993-1994 Research at the Center for Composite Materials, University of Delaware, USA (ccm.udel.edu), SNSF grant Since 1994 Research and teaching at EPFL, Composites, (LTC, LPAC) 1995-1999 Coordination Swiss Priority Program on Materials research: 2.2: Composites Since 1998 Biocomposites 2004-2009 Direction of the EPFL Transdisciplinary programme in Sport and Rehabilitation 2005-2008 Member of the EPFL Vice-Presidency for Innovation and Valorisation and direction a.i.EPFL-LTC Since 2016 Direction Discovery Learning Labs Materials/Bioengineering and Engineering

Official source

Ontological neighbourhood

Mathematics

Geometry: Euclidean geometry

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.

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.

Catalan solid

In mathematics, a Catalan solid, or Archimedean dual, is a polyhedron that is dual to an Archimedean solid. There are 13 Catalan solids. They are named for the Belgian mathematician Eugène Catalan, who first described them in 1865. The Catalan solids are all convex. They are face-transitive but not vertex-transitive. This is because the dual Archimedean solids are vertex-transitive and not face-transitive. Note that unlike Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons.

Platonic hydrocarbon

In organic chemistry, a Platonic hydrocarbon is a hydrocarbon (molecule) whose structure matches one of the five Platonic solids, with carbon atoms replacing its vertices, carbon–carbon bonds replacing its edges, and hydrogen atoms as needed. Not all Platonic solids have molecular hydrocarbon counterparts; those that do are the tetrahedron (tetrahedrane), the cube (cubane), and the dodecahedron (dodecahedrane). Tetrahedrane Tetrahedrane (C4H4) is a hypothetical compound.

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