Forbidden crystal symmetry in mathematics and architecture
With Sir Roger Penrose

00:41
New building  Mathematical Institute, University of Oxford
New building  Mathematical Institute, University of Oxford 
03:37
Translational symmetry
Translational symmetry 
03:50
Rotational symmetry
Rotational symmetry 
09:35
5 and Penrose Tiling  Numberphile
5 and Penrose Tiling  Numberphile
Watch on YouTube 
14:22
Johannes Kepler
Johannes Kepler 
18:12
Robert Ammann
Robert Ammann 
19:30
Raphael Robinson
Raphael Robinson 
24:12
Escherization of a Penrose tiling
Escherization of a Penrose tiling 
24:49
Penrose chicken tilings
Penrose chicken tilings 
26:42
Moiré pattern
Moiré pattern 
29:13
Celebrating Crystallography animation
Celebrating Crystallography
Celebrating Crystallography animation 
32:37
Quasicrystals
Quasicrystals 
33:02
Nobel Awarded to Researcher Who Redefined Crystalline  wired.com
Nobel Awarded to Researcher Who Redefined Crystalline  wired.com 
35:12
Storey Hall, RMIT University, Building 16
Storey Hall, RMIT University, Building 16 
35:27
Storey Hall
Storey Hall 
36:00
Gravity Discovery Centre  gravitycentre.com.au
Gravity Discovery Centre  gravitycentre.com.au 
38:33
Simons Centre for Geometry and Physics
Simons Centre for Geometry and Physics 
41:54
Transbay transit center
Transbay transit center 
46:16
Maths in the City  Wadham College
Maths in the City  Wadham College 
56:00
Images of the completed Mathematics Institute in Oxford courtesy of Vanesa Penrose.
Images of the completed Mathematics Institute in Oxford courtesy of Vanesa Penrose. 
56:04
The Mathematical Institute at Oxford University
The Mathematical Institute at Oxford University 
57:45
Images of the completed Mathematics Institute in Oxford courtesy of Vanesa Penrose.
Images of the completed Mathematics Institute in Oxford courtesy of Vanesa Penrose.
About this video
Revealing forbidden symmetry
Sir Roger Penrose provides a unique insight into the "forbidden symmetry" of his famous penrose tiles and the use of nonrepeating patterns in design and architecture.
It is a rigorous mathematical theorem that the only crystallographic symmetries are 2fold, 3fold, 4fold, and 6fold symmetries.
Yet, since the 1970s 5fold, 8fold, 10fold and 12fold "almost" symmetric patterns have been exhibited, showing that such crystallographically "forbidden symmetries" are mathematically possible and deviate from exact symmetry by an arbitrarily small amount. Such patterns are often beautiful to behold and designs based on these arrangements have now been used in many buildings throughout the world.
In this Ri event Sir Roger Penrose reveals the mathematical underpinnings and origins of these "forbidden symmetries" and other related patterns. His talk is illustrated with numerous examples of their use in architectural design including a novel version of "Penrose tiling" that appears in the approach to the main entrance of the new Mathematics Institute in Oxford, officially opened in late 2013.
The tiling is constructed from several thousand diamondshaped granite tiles of just two different shapes, decorated simply with circular arcs of stainless steel. The matching of the tiles forces them into an overall pattern which never repeats itself and exhibits remarkable aspects of 5fold and 10fold symmetry.
Similar features have been found also in the atomic structures of quasicrystalline materials. The initial discovery of such material earned Dan Shectman the 2011 Nobel Prize for chemistry, his work having launched a completely novel area of crystallography.
Images of the completed Mathematics Institute in Oxford courtesy of Vanesa Penrose.
The filming and production of this event was supported by the Science and Technology Facilities Council.
Production by Edward Prosser. Additional camera operation by Mark Billy Svensson.
Watch the event Q&A
Themes
Details
 Type:
 Event
 Organisations/Partners:
 STFC
 People:
 Sir Roger Penrose
 Location:
 London, UK
 Filmed in:
 The Theatre
 Published:
 2014
 Filmed:
 2013
 Credits:
Royal Institution
 Collections with this video:
 Ri Talks, The Crystallography Collection
Licence: © The Royal Institution
Related Links and Media

Penrose tiling
Image: Wikimedia Commons
Licence:Penrose tiling
Image: Wikimedia Commons
Licence: 
Pemrose tiling
Image: Wikimedia Commons
Licence:Pemrose tiling
Image: Wikimedia Commons
Licence: 
A Penrose tiling using Penrose's original set of six tiles (the "P1" set).
Image: Wikimedia Commons
Licence:A Penrose tiling using Penrose's original set of six tiles (the "P1" set).
Image: Wikimedia Commons
Licence:
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