A377996 Decimal expansion of the dihedral angle, in radians, between triangular and square faces in a (small) rhombicosidodecahedron.

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

Offset: 1

Author

Paolo Xausa, Nov 15 2024

Keywords

• nonn
• cons
• easy

Comments

Also the dihedral angle, in radians, between square and hexagonal faces in a truncated icosidodecahedron (great rhombicosidodecahedron).

Examples

			2.7767288254763100567352450533728425364989164423512...
		

Links

• Eric Weisstein's World of Mathematics, Great Rhombicosidodecahedron.
• Eric Weisstein's World of Mathematics, Small Rhombicosidodecahedron.

Crossrefs

Cf. A002194, A010472, A377995.

Programs

Mathematica

First[RealDigits[ArcCos[-(Sqrt[3] + Sqrt[15])/6], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["Rhombicosidodecahedron", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos(-(sqrt(3) + sqrt(15))/6) = arccos(-(A002194 + A010472)/6).