A378714 Decimal expansion of the inradius of a disdyakis dodecahedron with unit shorter edge length.

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

Offset

1,2

Comments

The disdyakis dodecahedron is the dual polyhedron of the truncated cuboctahedron (great rhombicuboctahedron).

Links

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

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt((3/97)*(166 + 95*sqrt(2)))/2 = sqrt((3/97)*(166 + 95*A002193))/2.

Minimal polynomial: 776*x^4 - 1992*x^2 + 441. - Amiram Eldar, May 14 2026

Example

1.5239081483234575496935813294889545216581003925...

Mathematica

First[RealDigits[Sqrt[3/97*(166 + 95*Sqrt[2])]/2, 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["DisdyakisDodecahedron", "Inradius"], 10, 100]]

Prog

(PARI) sqrt((166 + 95*sqrt(2))*3/97)/2 \\ Charles R Greathouse IV, Feb 05 2025

Crossrefs

Cf. A378712 (surface area), A378713 (volume), A378393 (midradius), A378715 (dihedral angle).

Cf. A002193.

Sequence in context: A376913 A377088 A261026 * A160080 A026247 A354236

Adjacent sequences: A378711 A378712 A378713 * A378715 A378716 A378717

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 07 2024

Status

approved