Gillies' conjecture
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Gillies' conjecture | |
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(No image) | |
Type | Dual uniform honeycomb |
Coxeter-Dynkin diagrams | Template:CDD |
Cell | Phyllic disphenoid |
Faces | Rhombus Triangle |
Space group Fibrifold notation Coxeter notation |
[[Cubic crystal system|ImTemplate:Overlinem (229)]] 8o:2 [[4,3,4]] |
Coxeter group | [4,3,4], |
vertex figures | Template:CDD, Template:CDD |
Dual | Omnitruncated cubic honeycomb |
Properties | Cell-transitive, face-transitive |
The phyllic disphenoidal honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. John Horton Conway calls it an eighth pyramidille.
Related honeycombs
It is dual to the omnitruncated cubic honeycomb:
See also
References
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- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, (2008) The Symmetries of Things, ISBN 978-1-56881-220-5 (Chapter 21, Naming the Archimedean and Catalan polyhedra and tilings, Architectonic and Catoptric tessellations, p 292-298, includes all the nonprismatic forms)
- Branko Grünbaum, Uniform tilings of 3-space. Geombinatorics 4(1994), 49 - 56.