A384871 -id:A384871 - cp's OEIS frontend

A384872 Decimal expansion of the surface area of a pentagonal orthocupolarotunda with unit edge.

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

Offset: 2

Paolo Xausa, Jun 11 2025

The pentagonal orthocupolarotunda is Johnson solid J_32.

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

			23.538532332506058310041007622367288571887138891860...

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

Cf. A384871 (volume).

Cf. A002163, A002194, A384284, A384286, A384625.

First[RealDigits[5 + 15/4*Sqrt[3] + 7/4*Sqrt[25 + 10*Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J32", "SurfaceArea"], 10, 100]]

Equals 5 + (15/4)*sqrt(3) + (7/4)*sqrt(25 + 10*sqrt(5)) = 5 + (15/4)*A002194 + (7/4)*sqrt(25 + 10*A002163).

Equals the largest root of 256*x^8 - 10240*x^7 + 57600*x^6 + 1856000*x^5 - 21756000*x^4 + 6320000*x^3 + 484812500*x^2 - 364125000*x - 342171875.

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.

cp's OEIS Frontend

A384872 Decimal expansion of the surface area of a pentagonal orthocupolarotunda 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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