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

Eric Weisstein's World of Mathematics, Disdyakis Dodecahedron.

Wikipedia, Disdyakis dodecahedron.

Formula

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

Example

32.066734010531944413349823874895723462863495851553...

Mathematica

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

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 * A246834 A319730 A262294

Adjacent sequences: A378707 A378708 A378709 * A378713 A378714 A378715

Keyword

nonn,cons,easy,new

Author

Paolo Xausa, Dec 06 2024

Status

approved