A379386 -id:A379386 - cp's OEIS frontend

A379388 Decimal expansion of the midradius of a deltoidal hexecontahedron with unit shorter edge length.

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

Offset: 1

Paolo Xausa, Dec 23 2024

The deltoidal hexecontahedron is the dual polyhedron of the (small) rhombicosidodecahedron.

			2.70344418537486330266596288467532955303640193...

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

Cf. A379385 (surface area), A379386 (volume), A379387 (inradius), A379389 (dihedral angle).
Cf. A377795 (midradius of a (small) rhombicosidodecahedron with unit edge length).
Cf. A010532.

First[RealDigits[5/4 + 13/Sqrt[80], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DeltoidalHexecontahedron", "Midradius"], 10, 100]]

5/4 + 13/(4*sqrt(5)) \\ Charles R Greathouse IV, Feb 05 2025

Equals 5/4 + 13/(4*sqrt(5)) = 5/4 + 13/A010532.

A379385 Decimal expansion of the surface area of a deltoidal hexecontahedron with unit shorter edge length.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Dec 22 2024

The deltoidal hexecontahedron is the dual polyhedron of the (small) rhombicosidodecahedron.

			92.231912906404640710406169319098384407207052545184...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Eric Weisstein's World of Mathematics, Deltoidal Hexecontahedron.
Wikipedia, Deltoidal hexecontahedron.

Cf. A379386 (volume), A379387 (inradius), A379388 (midradius), A379389 (dihedral angle).
Cf. A344149 (surface area of a (small) rhombicosidodecahedron with unit edge length).
Cf. A002163.

First[RealDigits[Sqrt[4370 + 1850*Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DeltoidalHexecontahedron", "SurfaceArea"], 10, 100]]

Equals sqrt(4370 + 1850*sqrt(5)) = sqrt(4370 + 1850*A002163).

A379387 Decimal expansion of the inradius of a deltoidal hexecontahedron with unit shorter edge length.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Dec 23 2024

The deltoidal hexecontahedron is the dual polyhedron of the (small) rhombicosidodecahedron.

			2.634797688222471365013793337475980265570278715884...

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

Cf. A379385 (surface area), A379386 (volume), A379388 (midradius), A379389 (dihedral angle).

Cf. A002163.

First[RealDigits[Root[820*#^4 - 5710*#^2 + 121 &, 4], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DeltoidalHexecontahedron", "Inradius"], 10, 100]]

Equals 11*sqrt((135 + 59*sqrt(5))/205)/(7 - sqrt(5)) = 11*sqrt((135 + 59*A002163)/205)/(7 - A002163).

Equals the largest root of 820*x^4 - 5710*x^2 + 121.

A379389 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a deltoidal hexecontahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Dec 23 2024

The deltoidal hexecontahedron is the dual polyhedron of the (small) rhombicosidodecahedron.

			2.6899252342065763400728815146316168300353303724921...

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

Cf. A379385 (surface area), A379386 (volume), A379387 (inradius), A379388 (midradius).
Cf. A377995 and A377996 (dihedral angles of a (small) rhombicosidodecahedron).
Cf. A002163.

First[RealDigits[ArcCos[-(19 + 8*Sqrt[5])/41], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["DeltoidalHexecontahedron", "DihedralAngles"]], 10, 100]]

Equals arccos(-(19 + 8*sqrt(5))/41) = arccos(-(19 + 8*A002163)/41).

A380861 Decimal expansion of the smallest acute vertex angle, in radians, in a deltoidal hexecontahedron face.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Feb 06 2025

A deltoidal hexecontahedron face is a kite with one smallest acute angle (this constant), two largest acute angles (A380862) and one obtuse angle (A380863).

			1.1830367284200834147901361867998878650548206683684...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Deltoidal hexecontahedron.

Cf. A002163, A379385, A379386, A379387, A379388, A379389, A380862, A380863.

First[RealDigits[ArcCos[(9*Sqrt[5] - 5)/40], 10, 100]]

Equals arccos((9*sqrt(5) - 5)/40) = arccos((9*A002163 - 5)/40).

Equals 2*Pi - 2*A380862 - A380863.

A380862 Decimal expansion of the largest acute angles, in radians, in a deltoidal hexecontahedron face.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Feb 06 2025

A deltoidal hexecontahedron face is a kite with one smallest acute angle (A380861), two largest acute angles (this constant) and one obtuse angle (A380863).

			1.517985377460215463602191357386072448171233382527...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Deltoidal hexecontahedron.

Cf. A020762, A379385, A379386, A379387, A379388, A379389, A380861, A380863.

First[RealDigits[ArcCos[1/2 - 1/Sqrt[5]], 10, 100]]

Equals arccos(1/2 - 1/sqrt(5)) = arccos(1/2 - A020762).

Equals (2*Pi - A380861 - A380863)/2.

A380863 Decimal expansion of the obtuse vertex angle, in radians, in a deltoidal hexecontahedron face.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Feb 07 2025

A deltoidal hexecontahedron face is a kite with one smallest acute angle (A380861), two largest acute angles (A380862) and one obtuse angle (this constant).

			2.0641778238390721349307678649869730069970513653...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Deltoidal hexecontahedron.

Cf. A002163, A379385, A379386, A379387, A379388, A379389, A380861, A380862.

First[RealDigits[ArcCos[(-5 - 2*Sqrt[5])/20], 10, 100]]

Equals arccos((-5 - 2*sqrt(5))/20) = arccos((-5 - 2*A002163)/20).

Equals 2*Pi - A380861 - 2*A380862.

A382011 Decimal expansion of the isoperimetric quotient of a deltoidal hexecontahedron.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Mar 20 2025

For the definition of isoperimetric quotient of a solid, references and links, see A381684.

			0.94585201935672373543294815069379894720694870891...

Paolo Xausa, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers

Cf. A379385 (surface area), A379386 (volume).

Cf. A000796, A002163, A381684.

First[RealDigits[Pi/205*Sqrt[(78119 + 34912*Sqrt[5])/41], 10, 100]]

Equals 36*Pi*A379386^2/(A379385^3).

Equals (Pi/205)*sqrt((78119 + 34912*sqrt(5))/41) = (A000796/205)*sqrt((78119 + 34912*A002163)/41).

cp's OEIS Frontend

A379388 Decimal expansion of the midradius of a deltoidal hexecontahedron with unit shorter edge length.

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A379385 Decimal expansion of the surface area of a deltoidal hexecontahedron with unit shorter edge length.

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A379387 Decimal expansion of the inradius of a deltoidal hexecontahedron with unit shorter edge length.

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A379389 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a deltoidal hexecontahedron.

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A380861 Decimal expansion of the smallest acute vertex angle, in radians, in a deltoidal hexecontahedron face.

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A380862 Decimal expansion of the largest acute angles, in radians, in a deltoidal hexecontahedron face.

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A380863 Decimal expansion of the obtuse vertex angle, in radians, in a deltoidal hexecontahedron face.

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A382011 Decimal expansion of the isoperimetric quotient of a deltoidal hexecontahedron.