A395807 Decimal expansion of the circumradius of a uniform 10-gonal antiprism with unit edges.

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

Offset

1,2

Links

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

Polytope Wiki, Decagonal antiprism.

Eric Weisstein's World of Mathematics, Antiprism.

Wikipedia, Antiprism.

Index entries for algebraic numbers, degree 8.

Formula

Equals sqrt(4 + csc(Pi/20)^2)/4.

Equals sqrt((3 - 2*cos(Pi/10))/(8 - 8*cos(Pi/10))) = sqrt((3 - A188593)/(8 - 8*A019881)).

Equals sqrt(1 + (2*sqrt(5) + sqrt(50 + 22*sqrt(5)))/8) = sqrt(1 + (A010476 + sqrt(50 + 22*A002163))/8).

Equals the largest root of 256*x^8 - 1024*x^6 + 976*x^4 - 344*x^2 + 41.

Example

1.6745047437425603067556345281467845735161384284804...

Mathematica

First[RealDigits[Sqrt[4 + Csc[Pi/20]^2]/4, 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["DecagonalAntiprism", "Circumradius"], 10, 100]]

Crossrefs

Cf. A395804 (volume), A395805 (surface area), A395806 (midradius), A395946 (height).

Cf. A387607, A387610 (dihedral angles).

Cf. A002163, A010476, A019881, A188593.

Sequence in context: A362769 A195776 A092678 * A019932 A004447 A258989

Adjacent sequences: A395804 A395805 A395806 * A395809 A395810 A395811

Keyword

nonn,cons,easy

Author

Paolo Xausa, May 21 2026

Status

approved