A379134 -id:A379134 - cp's OEIS frontend

A379132 Decimal expansion of the surface area of a pentakis dodecahedron with unit shorter edge length.

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

Offset: 2

Paolo Xausa, Dec 16 2024

The pentakis dodecahedron is the dual polyhedron of the truncated icosahedron.

			27.93524960070079310581019127996368070525778610907...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.
Wikipedia, Pentakis dodecahedron.
Index entries for algebraic numbers, degree 4.

Cf. A379133 (volume), A379134 (inradius), A379135 (midradius), A379136 (dihedral angle).
Cf. A377750 (surface area of a truncated icosahedron with unit edge length).
Cf. A002163.

First[RealDigits[5/3*Sqrt[(421 + 63*Sqrt[5])/2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentakisDodecahedron", "SurfaceArea"], 10, 100]]

sqrt((421 + 63*sqrt(5))/2)*5/3 \\ Charles R Greathouse IV, Feb 05 2025

Equals (5/3)*sqrt((421 + 63*sqrt(5))/2) = (5/3)*sqrt((421 + 63*A002163)/2).

A379133 Decimal expansion of the volume of a pentakis dodecahedron with unit shorter edge length.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Dec 16 2024

The pentakis dodecahedron is the dual polyhedron of the truncated icosahedron.

			13.458569366318714223642964127539153595279924859762...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.
Wikipedia, Pentakis dodecahedron.
Index entries for algebraic numbers, degree 2.

Cf. A379132 (surface area), A379134 (inradius), A379135 (midradius), A379136 (dihedral angle).
Cf. A377751 (volume of a truncated icosahedron with unit edge length).
Cf. A002163.

First[RealDigits[5/36*(41 + 25*Sqrt[5]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentakisDodecahedron", "Volume"], 10, 100]]

(41 + 25*sqrt(5))*5/36 \\ Charles R Greathouse IV, Feb 05 2025

Equals (5/36)*(41 + 25*sqrt(5)) = (5/36)*(41 + 25*A002163).

A379135 Decimal expansion of the midradius of a pentakis dodecahedron with unit shorter edge length.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Dec 17 2024

The pentakis dodecahedron is the dual polyhedron of the truncated icosahedron.

			1.4756836610416140907689600838494857255268212565695...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.
Wikipedia, Pentakis dodecahedron.
Index entries for algebraic numbers, degree 2.

Cf. A379132 (surface area), A379133 (volume), A379134 (inradius), A379136 (dihedral angle).
Cf. A205769 (midradius + 1 of a truncated icosahedron with unit edge length).
Cf. A010499.

First[RealDigits[(11 + Sqrt[45])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentakisDodecahedron", "Midradius"], 10, 100]]

(11 + 3*sqrt(5))/12 \\ Charles R Greathouse IV, Feb 05 2025

Equals (11 + 3*sqrt(5))/12 = (11 + A010499)/12.

A379136 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a pentakis dodecahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Dec 17 2024

The pentakis dodecahedron is the dual polyhedron of the truncated icosahedron.

			2.7352547614903346619898560183934957927169693...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.
Wikipedia, Pentakis dodecahedron.

Cf. A379132 (surface area), A379133 (volume), A379134 (inradius), A379135 (midradius).
Cf. A236367 and A344075 (dihedral angles of a truncated icosahedron).
Cf. A002163.

First[RealDigits[ArcCos[-(80 + 9*Sqrt[5])/109], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["PentakisDodecahedron", "DihedralAngles"]], 10, 100]]

acos(-(80 + 9*sqrt(5))/109) \\ Charles R Greathouse IV, Feb 05 2025

Equals arccos(-(80 + 9*sqrt(5))/109) = arccos(-(80 + 9*A002163)/109).

cp's OEIS Frontend

A379132 Decimal expansion of the surface area of a pentakis dodecahedron with unit shorter edge length.

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A379133 Decimal expansion of the volume of a pentakis dodecahedron with unit shorter edge length.

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A379135 Decimal expansion of the midradius of a pentakis dodecahedron with unit shorter edge length.

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A379136 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a pentakis dodecahedron.

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