Top Qs
Timeline
Chat
Perspective

Fibrifold

From Wikipedia, the free encyclopedia

Remove ads

In mathematics, a fibrifold is (roughly) a fiber space whose fibers and base spaces are orbifolds. They were introduced by John Horton Conway, Olaf Delgado Friedrichs, and Daniel H. Huson et al. (2001), who introduced a system of notation for 3-dimensional fibrifolds and used this to assign names to the 219 affine space group types. 184 of these are considered reducible, and 35 irreducible.

Remove ads

Irreducible cubic space groups

Summarize
Perspective
Thumb
The 35/36 irreducible cubic space groups in fibrifold and international index and Hermann–Mauguin notation. 212 and 213 are enantiomorphous pairs giving the same fibrifold notation.

The 35 irreducible space groups correspond to the cubic space group.

35 irreducible space groups
8o:24:24o:24+:22:22o:22+:21o:2
8o44o4+22o2+1o
8o/44/44o/44+/42/42o/42+/41o/4
8−o8oo8+o4− −4−o4oo4+o4++2−o2oo2+o
More information Class Point group, Hexoctahedral *432 (m3m) ...
Thumb Thumb Thumb
8 primary hexoctahedral hextetrahedral lattices of the cubic space groups The fibrifold cubic subgroup structure shown is based on extending symmetry of the tetragonal disphenoid fundamental domain of space group 216, similar to the square

Irreducible group symbols (indexed 195−230) in Hermann–Mauguin notation, Fibrifold notation, geometric notation, and Coxeter notation:

More information Class (Orbifold point group), Space groups ...
Remove ads

References

  • Conway, John Horton; Delgado Friedrichs, Olaf; Huson, Daniel H.; Thurston, William P. (2001), "On three-dimensional space groups", Beiträge zur Algebra und Geometrie, 42 (2): 475–507, ISSN 0138-4821, MR 1865535
  • Hestenes, David; Holt, Jeremy W. (February 2007), "The Crystallographic Space Groups in Geometric Algebra" (PDF), Journal of Mathematical Physics, 48 (2): 023514, Bibcode:2007JMP....48b3514H, doi:10.1063/1.2426416
  • Conway, John H.; Burgiel, Heidi; Goodman-Strauss, Chaim (2008), The Symmetries of Things, Taylor & Francis, ISBN 978-1-56881-220-5, Zbl 1173.00001
  • Coxeter, H.S.M. (1995), "Regular and Semi Regular Polytopes III", in Sherk, F. Arthur; McMullen, Peter; Thompson, Anthony C.; et al. (eds.), Kaleidoscopes: Selected Writings of H.S.M. Coxeter, Wiley, pp. 313–358, ISBN 978-0-471-01003-6, Zbl 0976.01023


Remove ads
Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.

Remove ads