| 词条 | Triakis truncated tetrahedral honeycomb | ||||||||||||||
| 释义 |
The triakis truncated tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of triakis truncated tetrahedra. It was discovered in 1914.[1][2] Voronoi tessellationIt is the Voronoi tessellation of the carbon atoms in diamond,[3][4] which lie in the diamond cubic crystal structure. Being composed entirely of triakis truncated tetrahedra, it is cell-transitive. Relation to quarter cubic honeycombIt can be seen as the uniform quarter cubic honeycomb where its tetrahedal cells are subdivided by the center point into 4 shorter tetrahedra, and each adjoined to the adjacent truncated tetrahedral cells. See also
References1. ^{{cite journal|first1=L.|last1=Föppl|year=1914|title=Der Fundamentalbereich des Diamantgitters|journal=Phys. Z.|volume=15|pages=191–193}} {{Polychora-stub}}2. ^{{cite journal|last1=Grünbaum|first1=B.|last2=Shephard|first2=G. C.|title=Tilings with Congruent Tiles|journal=Bull. Amer. Math. Soc.|volume=3|issue=3|pages=951–973|year=1980|url=http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bams/1183547682|doi=10.1090/s0273-0979-1980-14827-2}} 3. ^{{cite web|last=Conway|first=John|title=Voronoi Polyhedron|url=https://groups.google.com/forum/?fromgroups=#!msg/geometry.puzzles/pkL3avbWPoc/ABSaqdQaqu4J|work=geometry.puzzles|accessdate=20 September 2012}} 4. ^{{cite book|last1=Conway|first1=John H.|last2=Burgiel|first2=Heidi|last3=Goodman-Strauss|first3=Chaim|title=The Symmetries of Things|page=332|year=2008|isbn=978-1568812205}} 2 : Honeycombs (geometry)|Truncated tilings |
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