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A377969
Decimal expansion of the dihedral angle, in radians, between triangular faces in a snub cube.
2
2, 6, 7, 4, 4, 4, 8, 0, 8, 3, 5, 3, 5, 2, 2, 8, 6, 8, 1, 5, 5, 6, 7, 4, 0, 8, 5, 5, 8, 5, 8, 7, 2, 8, 6, 4, 0, 9, 8, 5, 2, 2, 4, 9, 9, 7, 0, 6, 2, 2, 7, 6, 3, 8, 2, 4, 8, 0, 0, 6, 2, 7, 6, 5, 8, 2, 4, 2, 6, 4, 5, 6, 6, 4, 1, 2, 3, 4, 7, 1, 5, 1, 0, 4, 9, 8, 1, 5, 7, 3
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Snub Cube.
FORMULA
Equals 2*arcsec(sqrt(12*A377604^2 - 3)).
Equals Pi - arccos((2*A058265 - 1)/3).
Equals Pi - arccos(c), where c is the real root of 27*x^3 + 9*x^2 - 15*x - 13.
EXAMPLE
2.674448083535228681556740855858728640985224997062...
MATHEMATICA
First[RealDigits[Pi - ArcCos[Root[27*#^3 + 9*#^2 - 15*# - 13 &, 1]], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["SnubCube", "DihedralAngles"]], 10, 100]]
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Nov 13 2024
STATUS
approved