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A160247
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Table read by antidiagonals of "less regular type 1" truncated octahedron numbers built from face-centered-cubic sphere packing.
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0
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1, 13, 6, 55, 38, 19, 147, 116, 79, 44, 309, 260, 201, 140, 85, 561, 490, 405, 314, 225, 146, 923, 826, 711, 586, 459, 338, 231, 1415, 1288, 1139, 976, 807, 640, 483, 344
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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The sequence contains regular cuboctahedra (A005902) on the x-axis, regular octahedra (A005900) on the y-axis, and regular truncated octahedra (A005910) on the diagonal. As for the rest, they each have 6 squares of the same area, while the 8 hexagons (of another same area) have 2 side lengths which alternate.
The x-axis represents an increasing degree of truncation, while the y-axis represents an increasing quantity of units on the remaining original octahedron edge.
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REFERENCES
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Main Title: Polyhedra primer / Peter Pearce and Susan Pearce. Published/Created: New York : Van Nostrand Reinhold, c1978. Description: viii, 134 p. : ill. ; 24 cm. ISBN: 0442264968
Main Title: The book of numbers / John H. Conway, Richard K. Guy. Published/Created: New York, NY : Copernicus c1996. Description: ix, 310 p. : ill. (some col.) ; 24 cm. ISBN: 038797993X
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LINKS
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FORMULA
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v=(2*y^3+10*x^3+12*y^2x+24*Y*x^2-12*y^2-39*x^2-48*y*x+25*y+47*x-18)/3
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PROG
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(Excel) Paste the following formula into cell C3, and fill down and right to desired table size. All volumes 10, 000 and under are covered by column Q and row 27.
=(2*(ROW()-2)^3+10*(COLUMN()-2)^3+12*(ROW()-2)^2*(COLUMN()-2)+24*(ROW()-2)*(COLUMN()-2)^2-12*(ROW()-2)^2-39*(COLUMN()-2)^2-48*(ROW()-2)*(COLUMN()-2)+25*(ROW()-2)+47*(COLUMN()-2)-18)/3
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CROSSREFS
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KEYWORD
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AUTHOR
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Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 05 2009, May 19 2009
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STATUS
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approved
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