

A160247


Table read by antidiagonals of "less regular type 1" truncated octahedron numbers built from facecenteredcubic sphere packing.


0



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
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OFFSET

1,2


COMMENTS

The sequence contains regular cuboctahedra (A005902) on the xaxis, regular octahedra (A005900) on the yaxis, 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 xaxis represents an increasing degree of truncation, while the yaxis represents an increasing quantity of units on the remaining original octahedron edge.


REFERENCES

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


LINKS



FORMULA

v=(2*y^3+10*x^3+12*y^2x+24*Y*x^212*y^239*x^248*y*x+25*y+47*x18)/3


PROG

(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)^212*(ROW()2)^239*(COLUMN()2)^248*(ROW()2)*(COLUMN()2)+25*(ROW()2)+47*(COLUMN()2)18)/3


CROSSREFS



KEYWORD



AUTHOR

Chris G. SpiesRusk (chaosorder4(AT)gmail.com), May 05 2009, May 19 2009


STATUS

approved



