A319587 - OEIS

%I #19 May 23 2022 16:36:59

%S 3,261,110912,17895697067018274

%N The number of distinct solid nets of the six convex regular 4D-polytopes in the order of their 3D-cell count.

%C These values have been taken from the Buekenhout (1998) paper (see link). During the unfolding of these solid nets along their common face, the possibility of any overlapping is ignored.

%C This finite sequence is fully determined but a(5) and a(6) are too large to be displayed in data. See formulas below to calculate these terms.

%H Andrey Zabolotskiy, <a href="/A319587/b319587.txt">Table of n, a(n) for n = 1..6</a>

%H F. Buekenhout and M. Parker, <a href="https://doi.org/10.1016/S0012-365X(97)00225-2">The number of nets of the regular convex polytopes in dimension >= 4</a>, Discrete Mathematics 186 (1998) 69-94.

%F a(1) = 3;

%F a(2) = (82944 + 12*16 + 24*8 + 4*2304 + 6*128 + 12*96 + 12*192 + 12*288)/(2^7 * 3) = 261;

%F a(3) = 2^5*(2^7 * 3^3 + 1 + 3^2) = 110912;

%F a(4) = 6*(2^19 * 5688888889 + 347) = 17895697067018274;

%F 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);

%F a(6) = 2^188 * 3^102 * 5^20 * 7^36 * 11^48 * 23^48 * 29^30.

%t {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}

%Y Cf. A091159, A201187.

%K nonn,fini

%O 1,1

%A _Frank M Jackson_, Sep 23 2018