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

Author

Paolo Xausa, Dec 16 2024

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			27.93524960070079310581019127996368070525778610907...
		

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.

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.

Programs

Mathematica

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

PARI

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

Formula

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