A377970 Decimal expansion of the dihedral angle, in radians, between triangular and square faces in a snub cube.

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

Author

Paolo Xausa, Nov 13 2024

Keywords

• nonn
• cons
• easy

Examples

			2.4955316305777334348382341626778898107867306036053...
		

Links

• Eric Weisstein's World of Mathematics, Snub Cube.

Crossrefs

Cf. A058265, A377602, A377603, A377604, A377605, A377969.

Programs

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]]

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.