A397543 Decimal expansion of the surface area of a canonical (dual-uniform) pentagonal trapezohedron with unit short edge length.

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

Offset

2,1

Comments

The pentagonal trapezohedron is the dual polyhedron of the pentagonal antiprism.

Links

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

David I. McCooey, Pentagonal Trapezohedron.

Polytope Wiki, Pentagonal antitegum.

Eric Weisstein's World of Mathematics, Trapezohedron.

Wikipedia, Pentagonal trapezohedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals 5*(1 + s)^2*sqrt((1 - s)/2 + s + 2)/4, where s = sqrt(5) = A002163.

Equals the largest root of x^4 - 625*x^2 + 3125.

Example

24.898982848827802734015846213978370554090497058946...

Mathematica

First[RealDigits[Root[#^4 - 625*#^2 + 3125 &, 4], 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData[{"Trapezohedron", 5}, "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A384871 (volume), A237603 (inradius), A239798 (midradius), A397544 (height).

Cf. A104457 (long edge).

Cf. A019692 (small face angle * 10), A228719 (large face angle), A137218 (dihedral angle).

Cf. A384625 (surface area of the dual + 10).

Cf. A002163.

Sequence in context: A341107 A388196 A344075 * A011402 A379076 A131625

Adjacent sequences: A397540 A397541 A397542 * A397544 A397545 A397547

Keyword

nonn,cons,easy,new

Author

Paolo Xausa, Jun 30 2026

Status

approved