A385506 -id:A385506 - cp's OEIS frontend

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

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

Paolo Xausa, Jul 28 2025

The triaugmented truncated dodecahedron is Johnson solid J_71.

			92.01180051437046094749799835011671208159334626...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Wikipedia, Triaugmented truncated dodecahedron.

Cf. A386545 (surface area).

Cf. A002163, A179590, A377695, A385506, A385804, A386464, A386466.

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

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.

A385505 Decimal expansion of the volume of a biaugmented triangular prism with unit edge.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Jul 01 2025

The biaugmented triangular prism is Johnson solid J_50.

			0.90441722268325100631575782677970078459225860524491...

Paolo Xausa, Table of n, a(n) for n = 0..10000
Wikipedia, Biaugmented triangular prism.

Cf. A384141 (surface area + 4).

Cf. A020763, A385506.

First[RealDigits[Sqrt[59/144 + 1/Sqrt[6]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J50", "Volume"], 10, 100]]

Equals sqrt(59/144 + 1/sqrt(6)) = sqrt(59/144 + A020763).

Equals the largest root of 20736*x^4 - 16992*x^2 + 25.

A385569 Decimal expansion of the volume of an augmented hexagonal prism with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 03 2025

The augmented hexagonal prism is Johnson solid J_54.

			2.8337784717488317817581176329604248968424865266117...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Augmented hexagonal prism.

Cf. A354129 (surface area + 2).

Cf. A002193, A002194, A385505, A385506, A385509.

First[RealDigits[(Sqrt[2] + 9*Sqrt[3])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J54", "Volume"], 10, 100]]

Equals (sqrt(2) + 9*sqrt(3))/6 = (A002193 + 9*A002194)/6.

Equals the largest root of 1296*x^4 - 17640*x^2 + 58081.

A097715 Decimal expansion of 7*sqrt(3)/2.

Original entry on oeis.org

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

Offset: 1

Lekraj Beedassy, Sep 21 2004

Corresponds to the minimal height-to-diameter ratio of a cylinder such that seven of them may be placed in mutual contact.

Also the surface area of a triaugmented triangular prism (Johnson solid J_51) with unit edge. - Paolo Xausa, Jul 01 2025

			6.0621778264910705273460621952705532842998183883363...

Martin Gardner, The Scientific American book of Mathematical Puzzles & Diversions, pp. 115 Simon & Shuster NY 1959 (or Hexaflexagons And Other Mathematical Diversions, The Univ. of Chicago Press Chicago IL 1988).

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Triaugmented triangular prism.

Cf. A002194, A385506.

Mathematica
```
RealDigits[7Sqrt[3]/2, 10, 105][[1]]
```

Corrected and extended by Rick L. Shepherd and Ray Chandler, Sep 21 2004

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A385505 Decimal expansion of the volume of a biaugmented triangular prism with unit edge.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A385569 Decimal expansion of the volume of an augmented hexagonal prism with unit edge.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A097715 Decimal expansion of 7*sqrt(3)/2.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

Extensions