login
A377997
Decimal expansion of the dihedral angle, in radians, between triangular faces in a snub dodecahedron.
2
2, 8, 6, 5, 4, 0, 0, 6, 8, 8, 3, 4, 4, 7, 2, 8, 6, 0, 7, 6, 0, 4, 6, 0, 7, 3, 4, 1, 7, 3, 3, 6, 5, 6, 9, 1, 4, 1, 1, 9, 0, 0, 9, 6, 7, 2, 6, 6, 5, 2, 3, 7, 9, 6, 9, 0, 5, 9, 9, 2, 8, 5, 2, 5, 2, 2, 0, 3, 5, 8, 6, 9, 8, 3, 4, 3, 4, 2, 9, 0, 1, 8, 5, 7, 2, 8, 8, 7, 8, 0
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Snub Dodecahedron.
Wikipedia, Snub dodecahedron.
FORMULA
Equals Pi - arccos((2/3)*A377849 + 1/3).
Equals Pi - arccos(c), where c is the largest real root of 729*x^6 + 486*x^5 - 729*x^4 - 756*x^3 + 63*x^2 + 270*x + 1.
EXAMPLE
2.8654006883447286076046073417336569141190096726652...
MATHEMATICA
First[RealDigits[Pi - ArcCos[2*Root[#^3 + 2*#^2 - GoldenRatio^2 &, 1]/3 + 1/3], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["SnubDodecahedron", "DihedralAngles"]], 10, 100]]
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Nov 15 2024
STATUS
approved