Gillies' conjecture

Gillies' conjecture
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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], ${\tilde {C}}_{3}$
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

• Architectonic and catoptric tessellation

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.