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

2,2

Comments

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

Links

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

Eric Weisstein's World of Mathematics, Disdyakis Dodecahedron.

Wikipedia, Disdyakis dodecahedron.

Index entries for algebraic numbers, degree 4.

Formula

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

Minimal polynomial: 49*x^4 - 13164*x^2 + 43218. - Amiram Eldar, May 14 2026

Example

16.288919082923525038503122503619441045996797447357...

Mathematica

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

Prog

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

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.

Sequence in context: A259931 A333350 A332092 * A021163 A114866 A384279

Adjacent sequences: A378710 A378711 A378712 * A378714 A378715 A378716

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 07 2024

Status

approved