A384910 -id:A384910 - cp's OEIS frontend

A384911 Decimal expansion of the surface area of an elongated pentagonal orthocupolarotunda with unit edge.

3, 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 13 2025

The elongated pentagonal orthocupolarotunda is Johnson solid J_40.

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

			33.538532332506058310041007622367288571887138891860...

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

Cf. A384910 (volume).
Cf. A002163, A384284, A384286, A384625.
Apart from the leading digit the same as A384872.

First[RealDigits[(60 + Sqrt[10*(190 + 49*Sqrt[5] + 21*Sqrt[75 + 30*Sqrt[5]])])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J40", "SurfaceArea"], 10, 100]]

Equals (60 + sqrt(10*(190 + 49*sqrt(5) + 21*sqrt(75 + 30*sqrt(5)))))/4 = (60 + sqrt(10*(190 + 49*A002163 + 21*sqrt(75 + 30*A002163))))/4.

Equals the largest root of 256*x^8 - 30720*x^7 + 1491200*x^6 - 37440000*x^5 + 509444000*x^4 - 3437040000*x^3 + 5993612500*x^2 + 44939625000*x - 172099671875.

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

A384911 Decimal expansion of the surface area of an elongated pentagonal orthocupolarotunda with unit edge.

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