A319587 The number of distinct solid nets of the six convex regular 4D-polytopes in the order of their 3D-cell count.
3, 261, 110912, 17895697067018274
Offset: 1
Links
- Andrey Zabolotskiy, Table of n, a(n) for n = 1..6
- F. Buekenhout and M. Parker, The number of nets of the regular convex polytopes in dimension >= 4, Discrete Mathematics 186 (1998) 69-94.
Programs
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Mathematica
{3, (82944+12*16+24*8+4*2304+6*128+12*96+12*192+12*288)/(2^7*3), 2^5(2^7*3^3+1+3^2), 6(2^19*5688888889+347), 2^7*5^2*7^3(2^114*3^78*5^20*7^33+2^47*3^18*5^2*7^12*53^5*2311^3+239^2*3931^2), 2^188*3^102*5^20*7^36*11^48*23^48*29^30}
Formula
a(1) = 3;
a(2) = (82944 + 12*16 + 24*8 + 4*2304 + 6*128 + 12*96 + 12*192 + 12*288)/(2^7 * 3) = 261;
a(3) = 2^5*(2^7 * 3^3 + 1 + 3^2) = 110912;
a(4) = 6*(2^19 * 5688888889 + 347) = 17895697067018274;
a(5) = 2^7 * 5^2 * 7^3 * (2^114 * 3^78 * 5^20 * 7^33 + 2^47 * 3^18 * 5^2 * 7^12 * 53^5 * 2311^3 + 239^2 * 3931^2);
a(6) = 2^188 * 3^102 * 5^20 * 7^36 * 11^48 * 23^48 * 29^30.
Comments