A334114 Decimal expansion of volume of a sphenomegacorona (J88) with each edge of unit length.
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, 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, 6, 2, 3, 8, 5, 0, 4, 7, 1, 5, 1, 9, 6, 4, 7, 1, 1, 7, 4
Offset: 1
Examples
1.94810822885947280327067639...
Links
- Violeta Hernández Palacios, Table of n, a(n) for n = 1..20000
- Norman W. Johnson, Convex Polyhedra with Regular Faces, Canadian Journal of Mathematics, 18 (1966), 169-200.
- H. S. Teoh, The Sphenomegacorona
- A. V. Timofeenko, The non-platonic and non-Archimedean noncomposite polyhedra, Journal of Mathematical Sciences, 162(2009), 720-722.
- Eric Weisstein's World of Mathematics, Sphenomegacorona.
Programs
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Mathematica
k := Root[-23 - 56 x + 200 x^2 + 304 x^3 - 776 x^4 + 240 x^5 + 2000 x^6 - 5584 x^7 - 3384 x^8 + 17248 x^9 + 2464 x^10 - 24576 x^11 + 1568 x^12 + 17216 x^13 - 3712 x^14 - 4800 x^15 + 1680 x^16, 2]; {{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)}}; v = Union[%, {1, -1, 1}*# & /@ %, {-1, 1, 1}*# & /@ %, {-1, -1, 1}*# & /@ %]; f := {{2, 3, 12, 11}, {2, 3, 10, 9}, {3, 12, 5}, {3, 10, 5}, {12, 5, 7}, {10, 5, 7}, {7, 12, 8}, {7, 10, 1}, {12, 8, 11}, {10, 1, 9}, {8, 1, 7}, {8, 1, 6}, {8, 11, 6}, {1, 9, 6}, {11, 6, 4}, {9, 6, 4}, {4, 11, 2}, {4, 9, 2}}; RealDigits[N[Volume[Polyhedron[v, f]], 20000]][[1]]
Comments