A379132 Decimal expansion of the surface area of a pentakis dodecahedron with unit shorter edge length.

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

Offset

2,1

Comments

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

Links

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

Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.

Wikipedia, Pentakis dodecahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals (5/3)*sqrt((421 + 63*sqrt(5))/2) = (5/3)*sqrt((421 + 63*A002163)/2).

Example

27.93524960070079310581019127996368070525778610907...

Mathematica

First[RealDigits[5/3*Sqrt[(421 + 63*Sqrt[5])/2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentakisDodecahedron", "SurfaceArea"], 10, 100]]

Prog

(PARI) sqrt((421 + 63*sqrt(5))/2)*5/3 \\ Charles R Greathouse IV, Feb 05 2025

Crossrefs

Cf. A379133 (volume), A379134 (inradius), A379135 (midradius), A379136 (dihedral angle).

Cf. A377750 (surface area of a truncated icosahedron with unit edge length).

Cf. A002163.

Sequence in context: A198122 A021362 A371803 * A246672 A011054 A276140

Adjacent sequences: A379129 A379130 A379131 * A379133 A379134 A379135

Keyword

nonn,cons,easy,changed

Author

Paolo Xausa, Dec 16 2024

Status

approved