A386852 -id:A386852 - cp's OEIS frontend

A386853 Decimal expansion of the dihedral angle, in radians, between the 10-gonal face and a triangular face in a pentagonal rotunda (Johnson solid J_6).

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

Offset: 1

Paolo Xausa, Aug 06 2025

			1.38208579601133454945018729145714326976181383401...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Pentagonal rotunda.
Index entries for transcendental numbers.

Cf. A179593 (volume), A179637 (surface area).
Cf. other J_6 dihedral angles: A105199, A344075.
Cf. A010476, A386852.

First[RealDigits[ArcCos[Sqrt[(5 - Sqrt[20])/15]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J6", "DihedralAngles"]], 2], 10, 100]]

acos(sqrt((5 - 2*sqrt(5))/15)) \\ Charles R Greathouse IV, Aug 19 2025

Equals arccos(sqrt((5 - 2*sqrt(5))/15)) = arccos(sqrt((5 - A010476)/15)).

A387189 Decimal expansion of the smallest dihedral angle, in radians, in a pentagonal bipyramid (Johnson solid J_13).

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 21 2025

This is the dihedral angle between triangular faces at the edge where the two pyramidal parts of the solid meet.

Also the dihedral angle between triangular faces in a pentagonal orthobicupola (Johnson solid J_30).

			1.3047162795687363719907812632876451487306158399...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Pentagonal bipyramid.
Wikipedia, Pentagonal orthobicupola.

Cf. A236367 (J_13 smallest dihedral angle).
Cf. other J_30 dihedral angles: A105199, A377995, A377996.
Cf. A179641 (J_13 volume), A120011 (J_13 surface area, divided by 10).
Cf. A384624 (J_30 volume), A384625 (J_30 surface area).
Cf. A010532, A386852.

First[RealDigits[ArcCos[(Sqrt[80] - 5)/15], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J13", "DihedralAngles"]], 10, 100]]

Equals arccos((4*sqrt(5) - 5)/15) = arccos((A010532 - 5)/15).

Equals 2*A386852.

cp's OEIS Frontend

A386853 Decimal expansion of the dihedral angle, in radians, between the 10-gonal face and a triangular face in a pentagonal rotunda (Johnson solid J_6).

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