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 1-3 of 3 results.

A386465 Decimal expansion of the surface area of an augmented truncated dodecahedron with unit edges.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 25 2025

Keywords

Comments

The augmented truncated dodecahedron is Johnson solid J_68.

Examples

			102.18209222021391857798854245281533205298421595361...

Links

Crossrefs

Cf. A386464 (volume).
Cf. A002194, A010476, A377694, A386412, A386460, A386543, A386545.

Programs

  • Mathematica
    First[RealDigits[(20 + 25*Sqrt[3] + 110*Sqrt[#] + Sqrt[5*#])/4 & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J68", "SurfaceArea"], 10, 100]]

Formula

Equals (20 + 25*sqrt(3) + 110*sqrt(5 + 2*sqrt(5)) + sqrt(5*(5 + 2*sqrt(5))))/4 = (20 + 25*A002194 + 110*sqrt(5 + A010476) + sqrt(5*(5 + A010476)))/4.
Equals the largest root of 256*x^8 - 10240*x^7 - 3955200*x^6 + 122240000*x^5 + 16152924000*x^4 - 343551280000*x^3 - 11461251137500*x^2 + 131995515375000*x + 634637481578125.

A386543 Decimal expansion of the surface area of a parabiaugmented truncated dodecahedron with unit edges.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 28 2025

Keywords

Comments

The parabiaugmented truncated dodecahedron is Johnson solid J_69.
Also the surface area of a metabiaugmented truncated dodecahedron (Johnson solid J_70) with unit edges.

Examples

			103.37342428732584861123113591699400755105334133204...

Links

Crossrefs

Cf. A386466 (volume).
Cf. A002194, A010476, A377694, A385803, A386465, A386545.

Programs

  • Mathematica
    First[RealDigits[(20 + 15*Sqrt[3] + 50*Sqrt[#] + Sqrt[5*#])/2 & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J69", "SurfaceArea"], 10, 100]]

Formula

Equals (20 + 15*sqrt(3) + 50*sqrt(5 + 2*sqrt(5)) + sqrt(5*(5 + 2*sqrt(5))))/2 = (20 + 15*A002194 + 50*sqrt(5 + A010476) + sqrt(5*(5 + A010476)))/2.
Equals the largest root of x^8 - 80*x^7 - 11400*x^6 + 796000*x^5 + 31475250*x^4 - 1804610000*x^3 - 8296459375*x^2 + 548931187500*x - 2544044046875.

A386544 Decimal expansion of the volume of a triaugmented truncated dodecahedron with unit edges.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 28 2025

Keywords

Comments

The triaugmented truncated dodecahedron is Johnson solid J_71.

Examples

			92.01180051437046094749799835011671208159334626...

Links

Crossrefs

Cf. A386545 (surface area).
Cf. A002163, A179590, A377695, A385506, A385804, A386464, A386466.

Programs

  • Mathematica
    First[RealDigits[7/12*(75 + 37*Sqrt[5]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J71", "Volume"], 10, 100]]

Formula

Equals (7/12)*(75 + 37*sqrt(5)) = (7/12)*(75 + 37*A002163).
Equals A377695 + 3*A179590.
Equals the largest root of 36*x^2 - 3150*x - 14945.
Showing 1-3 of 3 results.

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