A380002 -id:A380002 - cp's OEIS frontend

A380003 Decimal expansion of acute vertex angle, in radians, in a pentagonal hexecontahedron face.

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

Offset: 1

Paolo Xausa, Jan 12 2025

A pentagonal hexecontahedron face is an irregular pentagon with one acute angle (this constant) and four (equal) obtuse angles (A380004).

			1.1772858234717502919235374454812446809073054345981...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pentagonal Hexecontahedron.
Wikipedia, Pentagonal hexecontahedron.

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379890 (midradius), A379892 (dihedral angle), A380002 (long/short edge length ratio), A380004 (face obtuse angles).

First[RealDigits[ArcCos[Root[64*#^6 - 384*#^5 + 384*#^4 + 888*#^3 + 168*#^2 - 128*# - 31 &, 4]], 10, 100]]

Equals arccos(c), where c is the largest real root of 64*x^6 - 384*x^5 + 384*x^4 + 888*x^3 + 168*x^2 - 128*x - 31.

Equals 3*Pi - 4*A380004.

A380004 Decimal expansion of obtuse vertex angles, in radians, in a pentagonal hexecontahedron face.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jan 12 2025

A pentagonal hexecontahedron face is an irregular pentagon with one acute angle (A380003) and four (equal) obtuse angles (this constant).

			2.06187303432440735586609817608931599292105069088...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pentagonal Hexecontahedron.
Wikipedia, Pentagonal hexecontahedron.

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379890 (midradius), A379892 (dihedral angle), A380002 (long/short edge length ratio), A380003 (face acute angle).

First[RealDigits[ArcCos[Root[64*#^6 - 128*#^5 + 64*#^4 + 24*#^3 - 24*#^2 + 1 &, 1]], 10, 100]]

Equals arccos(c), where c is the smallest real root of 64*x^6 - 128*x^5 + 64*x^4 + 24*x^3 - 24*x^2 + 1.

Equals (3*Pi - A380003)/4.

cp's OEIS Frontend

A380003 Decimal expansion of acute vertex angle, in radians, in a pentagonal hexecontahedron face.

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