A379135 Decimal expansion of the midradius of a pentakis dodecahedron with unit shorter edge length.

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

Offset

1,2

Comments

The pentakis dodecahedron is the dual polyhedron of the truncated icosahedron.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Polytope Wiki, Pentakis dodecahedron.

Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.

Wikipedia, Pentakis dodecahedron.

Index entries for algebraic numbers, degree 2.

Formula

Equals (11 + 3*sqrt(5))/12 = (11 + A010499)/12.

Minimal polynomial: 36*x^2 - 66*x + 19. - Amiram Eldar, May 17 2026

Example

1.4756836610416140907689600838494857255268212565695...

Mathematica

First[RealDigits[(11 + Sqrt[45])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentakisDodecahedron", "Midradius"], 10, 100]]

Prog

(PARI) (11 + 3*sqrt(5))/12 \\ Charles R Greathouse IV, Feb 05 2025

Crossrefs

Cf. A379132 (surface area), A379133 (volume), A379134 (inradius), A379136 (dihedral angle).

Cf. A205769 (midradius + 1 of a truncated icosahedron with unit edge length).

Cf. A010499.

Sequence in context: A086202 A107824 A085674 * A393691 A200391 A357483

Adjacent sequences: A379132 A379133 A379134 * A379136 A379137 A379138

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 17 2024

Status

approved