A378713 Decimal expansion of the volume of a disdyakis dodecahedron with unit shorter edge length.

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

Offset: 2

Author

Paolo Xausa, Dec 07 2024

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			16.288919082923525038503122503619441045996797447357...
		

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. A378712 (surface area), A378714 (inradius), A378393 (midradius), A378715 (dihedral angle).

Cf. A377344 (volume of a truncated cuboctahedron (great rhombicuboctahedron) with unit edge length).

Cf. A002193.

Programs

Mathematica

First[RealDigits[Sqrt[6582 + 4539*Sqrt[2]]/7, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DisdyakisDodecahedron", "Volume"], 10, 100]]

PARI

sqrt(3*(2194 + 1513*sqrt(2)))/7 \\ Charles R Greathouse IV, Feb 05 2025

Formula

Equals sqrt(3*(2194 + 1513*sqrt(2)))/7 = sqrt(6582 + 4539*A002193)/7.