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A334114 Decimal expansion of volume of a sphenomegacorona (J88) with each edge of unit length.

%I A334114 #29 Jan 06 2024 18:50:30
%S A334114 1,9,4,8,1,0,8,2,2,8,8,5,9,4,7,2,8,0,3,2,7,0,6,7,6,3,9,0,0,1,6,6,7,6,
%T A334114 4,1,4,1,8,4,7,8,0,8,1,3,5,6,2,7,4,6,3,7,5,5,3,6,7,6,3,3,7,6,0,0,9,5,
%U A334114 6,2,3,8,5,0,4,7,1,5,1,9,6,4,7,1,1,7,4
%N A334114 Decimal expansion of volume of a sphenomegacorona (J88) with each edge of unit length.
%C A334114 A sphenomegacorona is one of the 92 regular-faced non-isogonal convex polyhedra first enumerated by Norman W. Johnson. It's built out of 2 squares and 12 equilateral triangles.
%C A334114 This number is algebraic, of unknown degree.
%C A334114 It appears that the minimal polynomial is 521578814501447328359509917696*x^32 - 985204427391622731345740955648*x^30 - 16645447351681991898880656015360*x^28 + 79710816694053483249372512649216*x^26 - 152195045391070538203422101864448*x^24 + 156280253448056209478031589244928*x^22 - 96188116617075838858708654227456*x^20 + 30636368373570166303441645731840*x^18 + 5828527077458909552923002273792*x^16 - 8060049780765551057159394951168*x^14 + 1018074792115156107372011716608*x^12 + 35220131544370794950945931264*x^10 + 327511698517355918956755959808*x^8 - 116978732884218191486738706432*x^6 + 10231563774949176791703149568*x^4 - 366323949299263261553952192*x^2 + 3071435678740442112675625. - _Joerg Arndt_, Apr 16 2020
%H A334114 Violeta Hernández Palacios, <a href="/A334114/b334114.txt">Table of n, a(n) for n = 1..20000</a>
%H A334114 Norman W. Johnson, <a href="http://dx.doi.org/10.4153/CJM-1966-021-8">Convex Polyhedra with Regular Faces</a>, Canadian Journal of Mathematics, 18 (1966), 169-200.
%H A334114 H. S. Teoh, <a href="http://eusebeia.dyndns.org/4d/J88">The Sphenomegacorona</a>
%H A334114 A. V. Timofeenko, <a href="https://doi.org/10.1007/s10958-009-9655-0">The non-platonic and non-Archimedean noncomposite polyhedra</a>, Journal of Mathematical Sciences, 162(2009), 720-722.
%H A334114 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Sphenomegacorona.html">Sphenomegacorona</a>.
%e A334114 1.94810822885947280327067639...
%t A334114 k := Root[-23 - 56 x + 200 x^2 + 304 x^3 - 776 x^4 + 240 x^5 +
%t A334114    2000 x^6 - 5584 x^7 - 3384 x^8 + 17248 x^9 + 2464 x^10 -
%t A334114    24576 x^11 + 1568 x^12 + 17216 x^13 - 3712 x^14 - 4800 x^15 +
%t A334114    1680 x^16, 2];
%t A334114 {{0, 1/2, Sqrt[1 - k^2]}, {k, 1/2, 0}, {0, Sqrt[(3/4 - k^2)/(1 - k^2)] + 1/2, (1/2 - k^2)/Sqrt[1 - k^2]}, {1/2, 0, -Sqrt[1/2 + k - k^2]}, {0, (Sqrt[3/4 - k^2] (2 k^2 - 1))/((k^2 - 1) Sqrt[1 - k^2]) + 1/2, (k^4 - 1/2)/(1 - k^2)^(3/2)}};
%t A334114 v = Union[%, {1, -1, 1}*# & /@ %, {-1, 1, 1}*# & /@ %, {-1, -1,
%t A334114   1}*# & /@ %];
%t A334114 f := {{2, 3, 12, 11}, {2, 3, 10, 9}, {3, 12, 5}, {3, 10, 5}, {12, 5,
%t A334114   7}, {10, 5, 7}, {7, 12, 8}, {7, 10, 1}, {12, 8, 11}, {10, 1,
%t A334114   9}, {8, 1, 7}, {8, 1, 6}, {8, 11, 6}, {1, 9, 6}, {11, 6, 4}, {9,
%t A334114   6, 4}, {4, 11, 2}, {4, 9, 2}};
%t A334114 RealDigits[N[Volume[Polyhedron[v, f]], 20000]][[1]]
%Y A334114 Volumes of other Johnson solids: A179552, A179587, A179590.
%K A334114 nonn,cons
%O A334114 1,2
%A A334114 _Violeta Hernández Palacios_, Apr 14 2020