A377998 - OEIS

A377998

Decimal expansion of the dihedral angle, in radians, between triangular and pentagonal faces in a snub dodecahedron.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..90.

Eric Weisstein's World of Mathematics, Snub Dodecahedron.

Wikipedia, Snub dodecahedron.

FORMULA

Equals Pi - arccos(sqrt((12*phi - (4*phi + 8)*xi*(xi + 1) + 19)/15)), where phi = A001622 and xi = A377849.

Equals Pi - arccos(c), where c is the real root closest to 9/10 of 91125*x^12 - 668250*x^10 + 2006775*x^8 - 2735100*x^6 + 1768275*x^4 - 502410*x^2 + 43681.

EXAMPLE

2.669130633625756107707940935718208230518703745355...

MATHEMATICA

First[RealDigits[Pi - ArcCos[Root[91125*#^12 - 668250*#^10 + 2006775*#^8 - 2735100*#^6 + 1768275*#^4 - 502410*#^2 + 43681&, 7]], 10, 100]] (* or *)

First[RealDigits[Min[PolyhedronData["SnubDodecahedron", "DihedralAngles"]], 10, 100]]

CROSSREFS

Cf. A001622, A377804, A377805, A377806, A377807, A377849, A377997.

Sequence in context: A082911 A005869 A353624 * A372610 A021978 A141377

Adjacent sequences: A377995 A377996 A377997 * A377999 A378000 A378001

KEYWORD

nonn,cons,easy,new

AUTHOR

Paolo Xausa, Nov 15 2024

STATUS

approved