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URL: https://oeis.org/A394173

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A394173
Decimal expansion of the mean volume of a tetrahedron whose vertices are uniformly and independently selected at random in the interior of a truncated tetrahedron of unit volume.
7
0, 1, 4, 8, 4, 5, 1, 0, 1, 9, 0, 2, 8, 9, 5, 3, 7, 3, 0, 7, 2, 1, 7, 6, 2, 1, 1, 9, 0, 5, 0, 1, 2, 5, 1, 4, 0, 4, 6, 6, 4, 5, 2, 5, 1, 8, 9, 3, 9, 3, 0, 4, 5, 6, 6, 9, 1, 0, 3, 1, 9, 8, 2, 6, 1, 1, 7, 3, 8, 6, 4, 4, 3, 0, 1, 9, 0, 9, 6, 9, 1, 9, 2, 3, 1, 3, 0, 0, 3, 4, 0, 9, 0, 2, 4, 6, 2, 0, 4, 1, 5, 5, 9, 1, 6, 8
OFFSET
0,3
LINKS
Dominik Beck, On Random Simplex Picking Beyond the Blashke Problem, arXiv:2412.07952 [math.MG], 2024.
Dominik Beck, Random polytopes, doctoral thesis, Mathematical Institute of Charles University, Prague, 2025.
Eric Weisstein's World of Mathematics, Truncated Tetrahedron.
FORMULA
Equals 35604506258521/162358039443600 - 13447020779*Pi^2/96641690145 + 9972537226592*log(2)/3382459155075 + 3485442712*log(2)^2/1400604205 - 8953623027*log(3)/7884520175 - 53493528168*log(2)*log(3)/32213896715 + 53162662164*PolyLog(2, 1/4)/32213896715.
EXAMPLE
0.0148451019028953730721762119050125140466452518939304...
MATHEMATICA
RealDigits[35604506258521/162358039443600 - 13447020779*Pi^2/96641690145 + 9972537226592*Log[2]/3382459155075 + 3485442712*Log[2]^2/1400604205 - 8953623027*Log[3]/7884520175 - 53493528168*Log[2]*Log[3]/32213896715 + 53162662164*PolyLog[2, 1/4]/32213896715, 10, 120, -1][[1]]
PROG
(PARI) 35604506258521/162358039443600 - 13447020779*Pi^2/96641690145 + 9972537226592*log(2)/3382459155075 + 3485442712*log(2)^2/1400604205 - 8953623027*log(3)/7884520175 - 53493528168*log(2)*log(3)/32213896715 + 53162662164*polylog(2, 1/4)/32213896715
CROSSREFS
Tetrahedron volume in: A093524 (cube), A093525 (tetrahedron), A093591 (ball), A394169 (surface of sphere), A394170 (octahedron), A394171 (rhombic dodecahedron), A394172 (cuboctahedron), this constant (truncated tetrahedron), A394174 (triangular bipyramid), A394175 (triangular prism), A394176 (square pyramid).
Sequence in context: A045816 A085991 A122110 * A082632 A296481 A155874
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Mar 11 2026
STATUS
approved