A384138 -id:A384138 - cp's OEIS frontend

A384283 Decimal expansion of the volume of a gyroelongated pentagonal cupola with unit edge.

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

Offset: 1

Paolo Xausa, May 26 2025

The gyroelongated pentagonal cupola is Johnson solid J_24.

			9.07333319388018799314998398101816272215313393060...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Gyroelongated pentagonal cupola.
Index entries for algebraic numbers, degree 8

Cf. A384284 (surface area).

Cf. A002163, A010532, A179590, A179639, A179641, A384138, A384140, A384144, A384213.

First[RealDigits[(5 + Sqrt[80] + 5*Sqrt[2*(Sqrt[650 + 290*Sqrt[5]] - Sqrt[5] - 1)])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J24", "Volume"], 10, 100]]

(5 + 4*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 \\ Charles R Greathouse IV, Aug 19 2025

Equals (5 + 4*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (5 + A010532 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.

Equals the largest real root of 1679616*x^8 - 11197440*x^7 + 27060480*x^6 + 35769600*x^5 - 4456749600*x^4 - 10714248000*x^3 + 3828402000*x^2 + 13859430000*x + 5340175625.

A384140 Decimal expansion of the volume of an elongated pentagonal bipyramid with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, May 20 2025

The elongated pentagonal bipyramid is Johnson solid J_16.

			2.32348306538061606412644311644954928569409236664...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Elongated pentagonal bipyramid.

Cf. A384141 (surface area).

Cf. A002163, A383852, A384138, A384139.

First[RealDigits[(5 + Sqrt[5] + 3*Sqrt[25 + 10*Sqrt[5]])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J16", "Volume"], 10, 100]]

Equals (5 + sqrt(5) + 3*sqrt(25 + 10*sqrt(5)))/12 = (5 + A002163 + 3*sqrt(25 + 10*A002163))/12.

Equals the largest root of 20736*x^4 - 34560*x^3 - 44640*x^2 + 27600*x + 6025.

A384144 Decimal expansion of the volume of an elongated pentagonal cupola with unit edge.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, May 22 2025

The elongated pentagonal cupola is Johnson solid J_20.

			10.0182541612713266373651755525797920503105009319...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Wikipedia, Elongated pentagonal cupola.

Cf. A179591 (surface area - 10).

Cf. A010476, A010532, A384138, A384140, A384213.

First[RealDigits[(5 + Sqrt[80] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J20", "Volume"], 10, 100]]

Equals (5 + 4*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (5 + A010532 + 15*sqrt(5 + A010476))/6.

Equals the largest root of 324*x^4 - 1080*x^3 - 20340*x^2 - 18600*x + 49975.

A384213 Decimal expansion of the volume of an elongated pentagonal rotunda with unit edge.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, May 23 2025

The elongated pentagonal rotunda is Johnson solid J_21.

			14.611971811062835576338722470794915893557631368294...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Wikipedia, Elongated pentagonal rotunda.

Cf. A179637 (surface area - 10).

Cf. A002163, A010476, A384138, A384140, A384144.

First[RealDigits[(45 + 17*Sqrt[5] + 30*Sqrt[5 + Sqrt[20]])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J21", "Volume"], 10, 100]]

Equals (45 + 17*sqrt(5) + 30*sqrt(5 + 2*sqrt(5)))/12 = (45 + 17*A002163 + 30*sqrt(5 + A010476))/12.

Equals the largest real root of 1296*x^4 - 19440*x^3 + 2340*x^2 + 70200*x + 43525.

A384285 Decimal expansion of the volume of a gyroelongated pentagonal rotunda with unit edge.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, May 29 2025

The gyroelongated pentagonal rotunda is Johnson solid J_25.

			13.667050843671696932123530899233286565400264...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Wikipedia, Gyroelongated pentagonal rotunda.

Cf. A384286 (surface area).

Cf. A002163, A179590, A179639, A179641, A384138, A384140, A384144, A384213, A384283.

First[RealDigits[(45 + 17*# + 10*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/12 & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J25", "Volume"], 10, 100]]

Equals (45 + 17*sqrt(5) + 10*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/12 = (45 + 17*A002163 + 10*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/12.

Equals the largest real root of 1679616*x^8 - 50388480*x^7 + 603262080*x^6 - 3520972800*x^5 + 5215460400*x^4 + 4128624000*x^3 - 8894943000*x^2 + 3881385000*x - 424924375.

A384139 Decimal expansion of the volume of an elongated triangular bipyramid with unit edges.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, May 20 2025

The elongated triangular bipyramid is Johnson solid J_14.

Also the volume of an augmented triangular prism (Johnson solid J_49) with unit edges. - Paolo Xausa, Aug 04 2025

			0.66871496228773516484880970607808443816397995934875...

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

Cf. A165663 (surface area - 2).

Cf. A010482, A010482, A383852, A384138, A384140.

First[RealDigits[(Sqrt[8] + Sqrt[27])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J14", "Volume"], 10, 100]]

Equals (2*sqrt(2) + 3*sqrt(3))/12 = (A010466 + A010482)/12.

Equals the largest root of 20736*x^4 - 10080*x^2 + 361.

A387147 Decimal expansion of the dihedral angle, in radians, between triangular and square faces in an elongated pentagonal pyramid (Johnson solid J_9).

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 18 2025

Also one of the dihedral angles, in radians, in an elongated pentagonal bipyramid, elongated pentagonal cupola, elongated pentagonal orthobicupola, elongated pentagonal gyrobicupola, elongated pentagonal orthocupolarotunda and elongated pentagonal gyrocupolarotunda (Johnson solids J_16, J_20, J_38, J_39, J_40 and J_41, respectively).

			2.2231544665792648052267123232835740164638926196505...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Elongated pentagonal bipyramid.
Wikipedia, Elongated pentagonal cupola.
Wikipedia, Elongated pentagonal gyrobicupola.
Wikipedia, Elongated pentagonal gyrocupolarotunda.
Wikipedia, Elongated pentagonal orthobicupola.
Wikipedia, Elongated pentagonal orthocupolarotunda.
Wikipedia, Elongated pentagonal pyramid.
Index entries for transcendental numbers.

Cf. A384138 (J_9 volume).
Cf. other J_9 dihedral angles: A019669, A228719, A236367.
Cf. A010476.

First[RealDigits[ArcCos[-Sqrt[(10 - Sqrt[20])/15]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J9", "DihedralAngles"]], 2], 10, 100]]

acos(-sqrt((10 - sqrt(20))/15)) \\ Charles R Greathouse IV, Aug 19 2025

Equals arccos(-sqrt((10 - 2*sqrt[5])/15)) = arccos(-sqrt((10 - A010476)/15)).

cp's OEIS Frontend

A384283 Decimal expansion of the volume of a gyroelongated pentagonal cupola with unit edge.

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A384140 Decimal expansion of the volume of an elongated pentagonal bipyramid with unit edge.

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A384144 Decimal expansion of the volume of an elongated pentagonal cupola with unit edge.

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A384213 Decimal expansion of the volume of an elongated pentagonal rotunda with unit edge.

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A384285 Decimal expansion of the volume of a gyroelongated pentagonal rotunda with unit edge.

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A384139 Decimal expansion of the volume of an elongated triangular bipyramid with unit edges.

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A387147 Decimal expansion of the dihedral angle, in radians, between triangular and square faces in an elongated pentagonal pyramid (Johnson solid J_9).

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