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A377970
Decimal expansion of the dihedral angle, in radians, between triangular and square faces in a snub cube.
2
2, 4, 9, 5, 5, 3, 1, 6, 3, 0, 5, 7, 7, 7, 3, 3, 4, 3, 4, 8, 3, 8, 2, 3, 4, 1, 6, 2, 6, 7, 7, 8, 8, 9, 8, 1, 0, 7, 8, 6, 7, 3, 0, 6, 0, 3, 6, 0, 5, 3, 1, 1, 6, 6, 1, 9, 1, 0, 9, 5, 2, 7, 3, 7, 3, 6, 2, 2, 9, 9, 0, 0, 3, 9, 0, 3, 2, 8, 8, 4, 4, 9, 5, 5, 8, 9, 7, 2, 0, 6
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Snub Cube.
FORMULA
Equals arcsec(sqrt(12*A377604^2 - 3)) + arcsec(sqrt(4*A377604^2 - 1)).
Equals Pi - arccos(sqrt(1 - 2/(3*A058265))).
Equals Pi - arccos(c), where c is the positive real root of 27*x^6 - 99*x^4 + 129*x^2 - 49.
EXAMPLE
2.4955316305777334348382341626778898107867306036053...
MATHEMATICA
First[RealDigits[Pi - ArcCos[Root[27*#^6 - 99*#^4 + 129*#^2 - 49 &, 2]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["SnubCube", "DihedralAngles"]], 10, 100]]
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Nov 13 2024
STATUS
approved