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

2,2

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Polytope Wiki, Deltoidal icositetrahedron.

Eric Weisstein's World of Mathematics, Deltoidal Icositetrahedron.

Wikipedia, Deltoidal icositetrahedron.

Index entries for algebraic numbers, degree 4.

Formula

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

Minimal polynomial: x^4 - 244*x^2 + 4802. - Amiram Eldar, May 17 2026

Example

14.9133887137863387908227981130654481094824451352...

Mathematica

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

Crossrefs

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

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

Cf. A002193.

Sequence in context: A276190 A011290 A196502 * A372859 A388865 A129971

Adjacent sequences: A378388 A378389 A378390 * A378392 A378393 A378394

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 30 2024

Status

approved