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

Author

Paolo Xausa, Dec 06 2024

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			32.066734010531944413349823874895723462863495851553...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Eric Weisstein's World of Mathematics, Disdyakis Dodecahedron.
• Wikipedia, Disdyakis dodecahedron.
• Index entries for algebraic numbers, degree 4.

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.

Programs

Mathematica

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

PARI

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

Formula

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