cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

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

Views

Author

Paolo Xausa, Dec 22 2024

Keywords

Comments

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

Examples

			92.231912906404640710406169319098384407207052545184...

Links

Crossrefs

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

Programs

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

Formula

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

A386690 Decimal expansion of the surface area of a diminished rhombicosidodecahedron with unit edges.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 29 2025

Keywords

Comments

The diminished rhombicosidodecahedron is Johnson solid J_76.
Also the surface area of a paragyrate diminished rhombicosidodecahedron, a metagyrate diminished rhombicosidodecahedron and a bigyrate diminished rhombicosidodecahedron (Johnson solids J_77, J_78 and J_79, respectively) with unit edges.

Examples

			58.11465077780005950750278197201400152953339093...

Links

Crossrefs

Cf. A386689 (volume).
Cf. A002194, A010476, A344149, A386692, A386694.

Programs

  • Mathematica
    First[RealDigits[25 + (15*Sqrt[3] + 10*Sqrt[#] + 11*Sqrt[5*#])/4 & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J76", "SurfaceArea"], 10, 100]]

Formula

Equals 25 + (15*sqrt(3) + 10*sqrt(5 + 2*sqrt(5)) + 11*sqrt(5*(5 + 2*sqrt(5))))/4 = 25 + (15*A002194 + 10*sqrt(5 + A010476) + 11*sqrt(5*(5 + A010476)))/4.
Equals the largest root of 256*x^8 - 51200*x^7 + 4070400*x^6 - 162560000*x^5 + 3311844000*x^4 - 27184400000*x^3 - 92251037500*x^2 + 2593051875000*x - 8774179671875.

A386692 Decimal expansion of the surface area of a parabidiminished rhombicosidodecahedron with unit edges.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 30 2025

Keywords

Comments

The parabidiminished rhombicosidodecahedron is Johnson solid J_80.
Also the surface area of a metabidiminished rhombicosidodecahedron and a gyrate bidiminished rhombicosidodecahedron (Johnson solids J_81 and J_82, respectively) with unit edges.

Examples

			56.9233187106881294742601885078353260314642655523...

Links

Crossrefs

Cf. A386691 (volume).
Cf. A002194, A010476, A344149, A386690, A386694.

Programs

  • Mathematica
    First[RealDigits[5/2*(8 + Sqrt[3] + 2*Sqrt[#] + Sqrt[5*#]) & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J80", "SurfaceArea"], 10, 100]]

Formula

Equals (5/2)*(8 + sqrt(3) + 2*sqrt(5 + 2*sqrt(5)) + sqrt(5*(5 + 2*sqrt(5)))) = (5/2)*(8 + A002194 + 2*sqrt(5 + A010476) + sqrt(5*(5 + A010476))).
Equals the largest root of x^8 - 160*x^7 + 9000*x^6 - 184000*x^5 - 828750*x^4 + 79100000*x^3 - 718984375*x^2 - 3800625000*x + 55781640625.

A386694 Decimal expansion of the surface area of a tridiminished rhombicosidodecahedron with unit edges.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 31 2025

Keywords

Comments

The tridiminished rhombicosidodecahedron is Johnson solid J_83.

Examples

			55.731986643576199441017595043656650533395140173888...

Links

Crossrefs

Cf. A386693 (volume).
Cf. A002194, A010476, A344149, A386690, A386692.

Programs

  • Mathematica
    First[RealDigits[(60 + 5*Sqrt[3] + 30*Sqrt[#] + 9*Sqrt[5*#])/4 & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J83", "SurfaceArea"], 10, 100]]

Formula

Equals (60 + 5*sqrt(3) + 30*sqrt(5 + 2*sqrt(5)) + 9*sqrt(5*(5 + 2*sqrt(5))))/4 = (60 + 5*A002194 + 30*sqrt(5 + A010476) + 9*sqrt(5*(5 + A010476)))/4.
Equals the largest root of 256*x^8 - 30720*x^7 + 844800*x^6 + 20736000*x^5 - 1109916000*x^4 + 6460560000*x^3 + 265641862500*x^2 - 4344667875000*x + 19010422828125.

A377795 Decimal expansion of the midradius of a (small) rhombicosidodecahedron with unit edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 08 2024

Keywords

Examples

			2.1762508994828215111000528659977678801980731915893...

Links

Crossrefs

Cf. A344149 (surface area), A185093 (volume), A179592 (circumradius), A377606 (Dehn invariant, negated).
Cf. A002163.

Programs

  • Mathematica
    First[RealDigits[Sqrt[5/2 + Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["Rhombicosidodecahedron", "Midradius"], 10, 100]]

Formula

Equals sqrt(5/2 + sqrt(5)) = sqrt(5/2 + A002163).

A381694 Decimal expansion of the isoperimetric quotient of a (small) rhombicosidodecahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Mar 08 2025

Keywords

Comments

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

Examples

			0.93899527411045014134237823698302012883610912007046...

Links

Crossrefs

Cf. A344149 (surface area), A185093 (volume).
Cf. A000796, A002163, A002194, A381684.

Programs

  • Mathematica
    First[RealDigits[4*Pi*(60 + 29*Sqrt[5])^2/(30 + Sqrt[75] + 3*Sqrt[25 + Sqrt[500]])^3, 10, 100]]

Formula

Equals 36*Pi*A185093^2/(A344149^3).
Equals 4*Pi*(60 + 29*sqrt(5))^2/((30 + 5*sqrt(3) + 3*sqrt(25 + 10*sqrt(5)))^3) = 4*A000796*(60 + 29*A002163)^2/((30 + 5*A002194 + 3*sqrt(25 + 10*A002163))^3).

A384952 Decimal expansion of the volume of an elongated pentagonal orthobirotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 20 2025

Keywords

Comments

The elongated pentagonal orthobirotunda is Johnson solid J_42.
Also the volume of an elongated pentagonal gyrobirotunda (Johnson solid J_43) with unit edge.

Examples

			21.52973477918753764625171850149755722709850737774...

Links

Crossrefs

Cf. A179451 (surface area - 10), A344149 (surface area + 20).
Cf. A002163, A010476, A384283, A384285, A384624, A384871, A384909, A384910.

Programs

  • Mathematica
    First[RealDigits[(45 + 17*Sqrt[5] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J42", "Volume"], 10, 100]]

Formula

Equals (45 + 17*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (45 + 17*A002163 + 15*sqrt(5 + A010476))/6.
Equals the largest root of 1296*x^4 - 38880*x^3 + 252360*x^2 - 329400*x - 332975.
Showing 1-7 of 7 results.

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