A377998 Decimal expansion of the dihedral angle, in radians, between triangular and pentagonal faces in a snub dodecahedron.

2, 6, 6, 9, 1, 3, 0, 6, 3, 3, 6, 2, 5, 7, 5, 6, 1, 0, 7, 7, 0, 7, 9, 4, 0, 9, 3, 5, 7, 1, 8, 2, 0, 8, 2, 3, 0, 5, 1, 8, 7, 0, 3, 7, 4, 5, 3, 5, 5, 3, 8, 0, 2, 7, 4, 2, 2, 3, 5, 0, 2, 7, 2, 6, 0, 4, 0, 0, 7, 4, 7, 2, 9, 1, 9, 0, 6, 4, 8, 3, 7, 6, 8, 8, 9, 1, 6, 5, 0, 7

Offset: 1

Author

Paolo Xausa, Nov 15 2024

Keywords

• nonn
• cons
• easy

Examples

			2.669130633625756107707940935718208230518703745355...
		

Links

• Eric Weisstein's World of Mathematics, Snub Dodecahedron.
• Wikipedia, Snub dodecahedron.

Crossrefs

Cf. A001622, A377804, A377805, A377806, A377807, A377849, A377997.

Programs

Mathematica

First[RealDigits[Pi - ArcCos[Root[91125*#^12 - 668250*#^10 + 2006775*#^8 - 2735100*#^6 + 1768275*#^4 - 502410*#^2 + 43681&, 7]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["SnubDodecahedron", "DihedralAngles"]], 10, 100]]

Formula

Equals Pi - arccos(sqrt((12*phi - (4*phi + 8)*xi*(xi + 1) + 19)/15)), where phi = A001622 and xi = A377849.

Equals Pi - arccos(c), where c is the real root closest to 9/10 of 91125*x^12 - 668250*x^10 + 2006775*x^8 - 2735100*x^6 + 1768275*x^4 - 502410*x^2 + 43681.