A394076 - OEIS

%I #15 May 22 2026 08:00:26

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

%T 1,1,5,2,7,2,3,7,2,6,2,5,3,3,3,4,0,0,1,3,4,5,5,7,2,4,5,3,1,0,7,1,8,4,

%U 6,8,9,0,0,0,5,1,7,7,4,7,8,2,1,7,9,7,4,1,9,0

%N Smallest dihedral angle, in radians, in a uniform heptagonal antiprism.

%C This is the dihedral angle between a triangular face and an heptagonal face.

%H Paolo Xausa, <a href="/A394076/b394076.txt">Table of n, a(n) for n = 1..10000</a>

%H David I. McCooey, <a href="https://dmccooey.com/polyhedra/HeptagonalAntiprism.html">Heptagonal Antiprism</a>.

%H Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Heptagonal_antiprism">Heptagonal antiprism</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Antiprism.html">Antiprism</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Antiprism">Antiprism</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals arccos(-tan(Pi/14)/sqrt(3)) = arccos(-A020760*A343059).

%F Equals arccos((cot(Pi/7) - csc(Pi/7))/sqrt(3)) = arccos((A178818-A121598)/A002194).

%F Equals arccos(c), where c = -0.131776... is the third smallest real root of 189*x^6 - 315*x^4 + 63*x^2 - 1.

%e 1.7029571531467470730450715262481241152723726253334...

%t First[RealDigits[ArcCos[-Tan[Pi/14]/Sqrt[3]], 10, 100]] (* or *)

%t First[RealDigits[Min[PolyhedronData["HeptagonalAntiprism", "DihedralAngles"]], 10, 100]]

%o (PARI) acos(-tan(Pi/14)/sqrt(3)) \\ _Charles R Greathouse IV_, May 13 2026

%Y Cf. A394077 (the other dihedral angle).

%Y Cf. A394071 (volume), A394072 (surface area), A394073 (midradius), A394074 (circumradius), A394075 (height).

%Y Cf. A002194, A020760, A121598, A178818, A343059.

%K nonn,cons,easy

%O 1,2

%A _Paolo Xausa_, Mar 19 2026