A378391 Decimal expansion of the volume of a deltoidal icositetrahedron with unit shorter edge length.

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

Offset: 2

Author

Paolo Xausa, Nov 30 2024

Keywords

• nonn
• cons
• easy

Comments

The deltoidal icositetrahedron is the dual polyhedron of the (small) rhombicuboctahedron.

Examples

			14.9133887137863387908227981130654481094824451352...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Eric Weisstein's World of Mathematics, Deltoidal Icositetrahedron.
• Wikipedia, Deltoidal icositetrahedron.
• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A378390 (surface area), A378392 (inradius), A378393 (midradius), A378394 (dihedral angle).

Cf. A343965 (volume of a (small) rhombicuboctahedron with unit edge).

Cf. A002193.

Programs

Mathematica

First[RealDigits[Sqrt[122 + 71*Sqrt[2]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DeltoidalIcositetrahedron", "Volume"], 10, 100]]

Formula

Equals sqrt(122 + 71*sqrt(2)) = sqrt(122 + 71*A002193).