A397610 Decimal expansion of the inradius of a canonical (dual-uniform) hexagonal trapezohedron with unit short edge length.

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

Offset

1,2

Comments

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

Links

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

David I. McCooey, Hexagonal Trapezohedron.

Polytope Wiki, Hexagonal antitegum.

Eric Weisstein's World of Mathematics, Trapezohedron.

Wikipedia, Hexagonal trapezohedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt(4 + 7/sqrt(3))/2 = sqrt(4 + 7/A002194)/2.

Equals the largest real root of 48*x^4 - 96*x^2 - 1.

Example

1.4178726921278387777407972015530448629768077439902...

Mathematica

First[RealDigits[Sqrt[4 + 7/Sqrt[3]]/2, 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData[{"Trapezohedron", 6}, "Inradius"], 10, 100]]

Crossrefs

Cf. A397608 (volume), A397609 (surface area), A397611 (midradius), A397612 (height).

Cf. A019973 (long edge).

Cf. A397613 (small face angle), A397614 (large face angle), A195698 (dihedral angle).

Cf. A002194.

Sequence in context: A253635 A078975 A349672 * A396025 A050411 A010643

Adjacent sequences: A397606 A397608 A397609 * A397611 A397612 A397613

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 04 2026

Status

approved