A395324 Decimal expansion of the length of the shorter edges of a polyhedron with 32 vertices with conjecturally maximum possible volume inscribed in the unit sphere.

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

Offset

0,1

Comments

The surface of the polyhedron consists of 60 congruent isosceles triangles, where the two equal sides are shorter with a length given by this sequence, and the third side is longer with a length given by A381264. See A179290 and A395323 for more information.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for algebraic numbers, degree 8.

Formula

Equals sqrt(2 - 2*sqrt((2*sqrt(5) + 5)/15)).

Minimal polynomial: 45*x^8 - 360*x^6 + 960*x^4 - 960*x^2 + 256. - Stefano Spezia, Apr 21 2026

Example

0.6408518201709875412850519828984...

Mathematica

First[RealDigits[Sqrt[2 - 2*Sqrt[(2*Sqrt[5] + 5)/15]], 10, 100]] (* Paolo Xausa, Apr 21 2026 *)

Crossrefs

Cf. A081314, A081366, A179290, A381264, A395323.

Sequence in context: A097047 A331421 A197581 * A323525 A166978 A356547

Adjacent sequences: A395321 A395322 A395323 * A395325 A395326 A395327

Keyword

nonn,cons

Author

Hugo Pfoertner, Apr 21 2026

Status

approved