A378826 Decimal expansion of the midradius of a pentagonal icositetrahedron with unit shorter edge length.

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

Offset: 1

Author

Paolo Xausa, Dec 10 2024

Keywords

• nonn
• cons
• easy

Comments

The pentagonal icositetrahedron is the dual polyhedron of the snub cube.

Examples

			2.101593893296299757309517286375546687971276345216...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A378823 (surface area), A378824 (volume), A378825 (inradius), A378827 (dihedral angle).

Cf. A377605 (midradius of a snub cube with unit edge length).

Cf. A058265.

Programs

Mathematica

First[RealDigits[Root[32*#^6 - 144*#^4 + 12*#^2 - 1 &, 2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalIcositetrahedron", "Midradius"], 10, 100]]

Formula

Equals (1 + s)/sqrt(2*(1 + s)*(1 - 2*s)), where s = (A058265 - 1)/2.

Equals the positive real root of 32*x^6 - 144*x^4 + 12*x^2 - 1.