Talk:Sphenomegacorona

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Polyhedra Start‑class

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Volume of sphenomegacorona of unit edge length edit

Latest comment: 4 years ago2 comments1 person in discussion

WolframAlpha gives its volume as 1.94833, but my calculations in both Mathematica and GeoGebra show that the actual number, rounded to 5 digits, should instead be 1.94811. If anyone wants to check, here is my Mathematica code, based on Timofeenko's paper on the references.

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]

v := {{0, 1, 2 Sqrt[1 - k^2]}, {0, -1, 2 Sqrt[1 - k^2]}, {2 k, 1, 0}, {2 k, -1, 0}, {-2 k, 1, 0}, {-2 k, -1, 0}, {0, Sqrt[(3 - 4 k^2)/(1 - k^2)] + 1, (1 - 2 k^2)/Sqrt[1 - k^2]}, {0, -Sqrt[(3 - 4 k^2)/(1 - k^2)] - 1, (1 - 2 k^2)/Sqrt[1 - k^2]}, {1, 0, -Sqrt[2 + 4 k - 4 k^2]}, {-1, 0, -Sqrt[2 + 4 k - 4 k^2]}, {0, (Sqrt[3 - 4 k^2] (2 k^2 - 1))/((k^2 - 1) Sqrt[1 - k^2]) + 1, (2 k^4 - 1)/(1 - k^2)^(3/2)}, {0, -(Sqrt[3 - 4 k^2] (2 k^2 - 1))/((k^2 - 1) Sqrt[1 - k^2]) - 1, (2 k^4 - 1)/(1 - k^2)^(3/2)}}

f := {{2, 4, 3, 1}, {5, 1, 2, 6}, {4, 9, 3}, {3, 9, 11}, {1, 7, 3}, {3, 7, 11}, {7, 1, 5}, {5, 7, 11}, {5, 10, 11}, {5, 10, 6}, {11, 10, 9}, {2, 6, 8}, {2, 4, 8}, {8, 12, 6}, {4, 8, 12}, {6, 12, 10}, {12, 10, 9}, {12, 4, 9}}

N[Volume[Polyhedron[v, f]]/8, 6]

I'm currently proposing the sequence of digits to the OEIS, so it can be used as a reference. – OfficialURL (talk) 14:48, 13 April 2020 (UTC)Reply

Reference added to A334114. – OfficialURL (talk) 13:45, 15 April 2020 (UTC)Reply

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