cp's OEIS Frontend

A387147 Decimal expansion of the dihedral angle, in radians, between triangular and square faces in an elongated pentagonal pyramid (Johnson solid J_9).

%I A387147 #12 Aug 19 2025 10:42:15
%S A387147 2,2,2,3,1,5,4,4,6,6,5,7,9,2,6,4,8,0,5,2,2,6,7,1,2,3,2,3,2,8,3,5,7,4,
%T A387147 0,1,6,4,6,3,8,9,2,6,1,9,6,5,0,5,3,2,6,5,2,2,8,2,2,0,0,2,4,2,8,6,0,0,
%U A387147 5,1,7,8,6,9,6,4,1,4,4,0,3,2,2,2,3,5,8,4,5,5
%N A387147 Decimal expansion of the dihedral angle, in radians, between triangular and square faces in an elongated pentagonal pyramid (Johnson solid J_9).
%C A387147 Also one of the dihedral angles, in radians, in an elongated pentagonal bipyramid, elongated pentagonal cupola, elongated pentagonal orthobicupola, elongated pentagonal gyrobicupola, elongated pentagonal orthocupolarotunda and elongated pentagonal gyrocupolarotunda (Johnson solids J_16, J_20, J_38, J_39, J_40 and J_41, respectively).
%H A387147 Paolo Xausa, <a href="/A387147/b387147.txt">Table of n, a(n) for n = 1..10000</a>
%H A387147 Wikipedia, <a href="https://en.wikipedia.org/wiki/Elongated_pentagonal_bipyramid">Elongated pentagonal bipyramid</a>.
%H A387147 Wikipedia, <a href="https://en.wikipedia.org/wiki/Elongated_pentagonal_cupola">Elongated pentagonal cupola</a>.
%H A387147 Wikipedia, <a href="https://en.wikipedia.org/wiki/Elongated_pentagonal_gyrobicupola">Elongated pentagonal gyrobicupola</a>.
%H A387147 Wikipedia, <a href="https://en.wikipedia.org/wiki/Elongated_pentagonal_gyrocupolarotunda">Elongated pentagonal gyrocupolarotunda</a>.
%H A387147 Wikipedia, <a href="https://en.wikipedia.org/wiki/Elongated_pentagonal_orthobicupola">Elongated pentagonal orthobicupola</a>.
%H A387147 Wikipedia, <a href="https://en.wikipedia.org/wiki/Elongated_pentagonal_orthocupolarotunda">Elongated pentagonal orthocupolarotunda</a>.
%H A387147 Wikipedia, <a href="https://en.wikipedia.org/wiki/Elongated_pentagonal_pyramid">Elongated pentagonal pyramid</a>.
%H A387147 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A387147 Equals arccos(-sqrt((10 - 2*sqrt[5])/15)) = arccos(-sqrt((10 - A010476)/15)).
%e A387147 2.2231544665792648052267123232835740164638926196505...
%t A387147 First[RealDigits[ArcCos[-Sqrt[(10 - Sqrt[20])/15]], 10, 100]] (* or *)
%t A387147 First[RealDigits[RankedMax[Union[PolyhedronData["J9", "DihedralAngles"]], 2], 10, 100]]
%o A387147 (PARI) acos(-sqrt((10 - sqrt(20))/15)) \\ _Charles R Greathouse IV_, Aug 19 2025
%Y A387147 Cf. A384138 (J_9 volume).
%Y A387147 Cf. other J_9 dihedral angles: A019669, A228719, A236367.
%Y A387147 Cf. A010476.
%K A387147 nonn,cons,easy
%O A387147 1,1
%A A387147 _Paolo Xausa_, Aug 18 2025