A384624 -id:A384624 - cp's OEIS frontend

A384625 Decimal expansion of the surface area of a pentagonal orthobicupola with unit edge.

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

Offset: 2

Paolo Xausa, Jun 05 2025

The pentagonal orthobicupola is Johnson solid J_30.

Also the surface area of a pentagonal gyrobicupola (Johnson solid J_31) with unit edge.

			17.771081820100127079336639808541900116171761474546...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Wikipedia, Pentagonal orthobicupola.
Wikipedia, Pentagonal gyrobicupola.

Cf. A384624 (volume).

Cf. A002163, A384284, A384286, A384872.

First[RealDigits[10 + Sqrt[5*(10 + Sqrt[5] + Sqrt[75 + 30*Sqrt[5]])/2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J30", "SurfaceArea"], 10, 100]]

Equals 10 + sqrt(5*(10 + sqrt(5) + sqrt(75 + 30*sqrt(5)))/2) = 10 + sqrt(5*(10 + A002163 + sqrt(75 + 30*A002163))/2).

Equals the largest root of x^8 - 80*x^7 + 2700*x^6 - 50000*x^5 + 552750*x^4 - 3710000*x^3 + 14628125*x^2 - 30562500*x + 25328125.

A384871 Decimal expansion of the volume of a pentagonal orthocupolarotunda with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jun 11 2025

The pentagonal orthocupolarotunda is Johnson solid J_32.

Also the volume of a pentagonal gyrocupolarotunda (Johnson solid J_33) with unit edge.

			9.2418082864578952008524451431901588238346215825240...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Pentagonal gyrocupolarotunda.
Wikipedia, Pentagonal orthocupolarotunda.

Cf. A384872 (surface area).

Cf. A002163, A384144, A384283, A384285, A384624.

First[RealDigits[5*(11 + 5*Sqrt[5])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J32", "Volume"], 10, 100]]

Equals (5/12)*(11 + 5*sqrt(5)) = (5/12)*(11 + 5*A002163).

Equals the largest root of 36*x^2 - 330*x - 25.

A384287 Decimal expansion of the volume of a square orthobicupola with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jun 05 2025

The square orthobicupola is Johnson solid J_28.

Also the volume of a square gyrobicupola (Johnson solid J_29) with unit edge.

			3.885618083164126731735584965612930771426229167169...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Square gyrobicupola.
Wikipedia, Square orthobicupola.

Cf. A010469 (surface area - 10).

Cf. A002193, A010487, A384624.

First[RealDigits[2 + Sqrt[32]/3, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J28", "Volume"], 10, 100]]

Equals 2 + (4/3)*sqrt(2) = 2 + (4/3)*A002193 = 2 + A010487/3.

Equals the largest root of 9*x^2 - 36*x + 4.

A384909 Decimal expansion of the volume of an elongated pentagonal orthobicupola with unit edge.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jun 12 2025

The elongated pentagonal orthobicupola is Johnson solid J_38.

Also the volume of an elongated pentagonal gyrobicupola (Johnson solid J_39) with unit edge.

			12.342299479604519768304624665067309540604246504993...

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

Cf. A384625 (surface area - 10).

Cf. A002163, A010476, A384283, A384624, A384871.

First[RealDigits[(10 + 8*Sqrt[5] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J38", "Volume"], 10, 100]]

Equals (10 + 8*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (10 + 8*A002163 + 15*sqrt(5 + A010476))/6.

Equals the largest root of 1296*x^4 - 8640*x^3 - 82440*x^2 - 109200*x + 76525.

A384910 Decimal expansion of the volume of an elongated pentagonal orthocupolarotunda with unit edge.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jun 13 2025

The elongated pentagonal orthocupolarotunda is Johnson solid J_40.

Also the volume of an elongated pentagonal gyrocupolarotunda (Johnson solid J_41) with unit edge.

			16.936017129396028707278171583282433383851376941...

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

Cf. A384911 (surface area).

Cf. A002163, A010476, A384283, A384285, A384624, A384871, A384909.

First[RealDigits[5/12*(11 + 5*Sqrt[5] + 6*Sqrt[5 + Sqrt[20]]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J40", "Volume"], 10, 100]]

Equals (5/12)*(11 + 5*sqrt(5) + 6*sqrt(5 + 2*sqrt(5))) = (5/12)*(11 + 5*A002163 + 6*sqrt(5 + A010476)).

Equals the largest root of 1296*x^4 - 23760*x^3 + 26100*x^2 + 84000*x - 111875.

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

Paolo Xausa, Jun 20 2025

The elongated pentagonal orthobirotunda is Johnson solid J_42.

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

			21.52973477918753764625171850149755722709850737774...

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

Cf. A179451 (surface area - 10), A344149 (surface area + 20).

Cf. A002163, A010476, A384283, A384285, A384624, A384871, A384909, A384910.

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

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.

A387189 Decimal expansion of the smallest dihedral angle, in radians, in a pentagonal bipyramid (Johnson solid J_13).

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 21 2025

This is the dihedral angle between triangular faces at the edge where the two pyramidal parts of the solid meet.

Also the dihedral angle between triangular faces in a pentagonal orthobicupola (Johnson solid J_30).

			1.3047162795687363719907812632876451487306158399...

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

Cf. A236367 (J_13 smallest dihedral angle).
Cf. other J_30 dihedral angles: A105199, A377995, A377996.
Cf. A179641 (J_13 volume), A120011 (J_13 surface area, divided by 10).
Cf. A384624 (J_30 volume), A384625 (J_30 surface area).
Cf. A010532, A386852.

First[RealDigits[ArcCos[(Sqrt[80] - 5)/15], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J13", "DihedralAngles"]], 10, 100]]

Equals arccos((4*sqrt(5) - 5)/15) = arccos((A010532 - 5)/15).

Equals 2*A386852.

cp's OEIS Frontend

A384625 Decimal expansion of the surface area of a pentagonal orthobicupola with unit edge.

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A384871 Decimal expansion of the volume of a pentagonal orthocupolarotunda with unit edge.

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A384287 Decimal expansion of the volume of a square orthobicupola with unit edge.

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A384909 Decimal expansion of the volume of an elongated pentagonal orthobicupola with unit edge.

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A384910 Decimal expansion of the volume of an elongated pentagonal orthocupolarotunda with unit edge.

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

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A387189 Decimal expansion of the smallest dihedral angle, in radians, in a pentagonal bipyramid (Johnson solid J_13).

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