A378712 Decimal expansion of the surface area of a disdyakis dodecahedron with unit shorter edge length.

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

Offset

2,1

Comments

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

Links

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

Polytope Wiki, Disdyakis dodecahedron.

Eric Weisstein's World of Mathematics, Disdyakis Dodecahedron.

Wikipedia, Disdyakis dodecahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals (6/7)*sqrt(783 + 436*sqrt(2)) = (6/7)*sqrt(783 + 436*A002193).

Minimal polynomial: 49*x^4 - 56376*x^2 + 6159888. - Amiram Eldar, May 17 2026

Example

32.066734010531944413349823874895723462863495851553...

Mathematica

First[RealDigits[6/7*Sqrt[783 + 436*Sqrt[2]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DisdyakisDodecahedron", "SurfaceArea"], 10, 100]]

Prog

(PARI) sqrt(783 + 436*sqrt(2))*6/7 \\ Charles R Greathouse IV, Feb 05 2025

Crossrefs

Cf. A378713 (volume), A378714 (inradius), A378393 (midradius), A378715 (dihedral angle).

Cf. A377343 (surface area of a truncated cuboctahedron (great rhombicuboctahedron) with unit edge length).

Cf. A002193.

Sequence in context: A049780 A159584 A257653 * A385577 A246834 A319730

Adjacent sequences: A378709 A378710 A378711 * A378713 A378714 A378715

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 06 2024

Status

approved