Platonic Solids, The / Octet for Truss and Comb

Synopsis

Two programmes for use with course units GE5 and GE6: 1) The Platonic Solids (25 min): Classifies the direct symmetry groups of five regular solids. Introduces them and shows how they are built up from their respective nets, investigates the duality that exists between the cube and the octahedron and between the dodicahedron and the icosahedron, and shows how this simplifies the classifying the groups. Looks at the direct symmetry group of the cube and then the dodecahedron, investigating the different axes of rotation, constructing a elegant way of labelling all the symmetries, and concluding that the direct symmetry group of the cube is isomorphic to S4 and the dodecahedron is isomorphic to A5;
2) Octet for Truss and Comb (31 min): Shows how the three-dimensional solids described in the unit on lattices fit together in three dimensions to give a space-filling system consisting of just one polyhedron infinitely rpeated throughout space. Examples of such systems include the so-called ‘octet truss’, much used in construction, which has cubic symmetry; the rhombic dodecahedron, which is the space dual of the above octet; the cube and its variations; the ‘other’ octet, also made from two tetrahedrons and one octahedron, which has hexagonal symmetry. As well as identifying the key features of these and why they completely fill space, the idea of how they are related to the idea of ‘closest possible packing’ for spheres is also considered.

Series

Groups and Geometry, Course M336

Language

English

Country

Great Britain

Medium

Video; Videocassette. Standard formats. col. 56 min.

Year of production

1994

Availability

Sale; 2000 sale: £85.00 (+VAT +p&p)

Subjects

Mathematics

Keywords

geometry; group theory; polyhedra

Production Company

Name

BBC Open University Productions

Distributor

Name

Open University Worldwide

Web

http://www.ouw.co.uk External site opens in new window

Phone

+44 (0) 1908 274066

Address

Walton Hall
Milton Keynes
MK7 6AA

Notes

NB. As of May 2016 Open University Worldwide are no longer distributing DVDs. They have posted this message on their website: ‘Unfortunately Open University Worldwide Limited has decided that product sales are no longer viable given the reduced funding to Higher Education institutions and diminishing demand for the products we have traditionally stocked. At present the Open University Students Association (OUSA) will continue to sell the "Good Study Guide", and we are in discussion with other possible distributors to continue to make The Open University’s products available for purchase. As soon as we have any information on other channels of distribution we will update this notice’. Some products are still available via second hand dealers on Amazon.co.uk