A002163 -id:A002163 - 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.

A385260 Decimal expansion of the volume of a gyroelongated pentagonal bicupola with unit edge.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jun 27 2025

The gyroelongated pentagonal bicupola is Johnson solid J_46.

			11.397378512213381124089433093505680212446879503678...

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

Cf. A385261 (surface area).

Cf. A002163, A384283, A385256, A385258.

First[RealDigits[(10 + 8*# + 5*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/6 & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J46", "Volume"], 10, 100]]

Equals (10 + 8*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (10 + 8*A002163 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.

Equals the largest real root of 6561*x^8 - 87480*x^7 + 313470*x^6 + 753300*x^5 - 22424850*x^4 - 84591000*x^3 - 85909500*x^2 + 8715000*x + 35547500.

A385261 Decimal expansion of the surface area of a gyroelongated pentagonal bicupola with unit edge.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jun 27 2025

The gyroelongated pentagonal bicupola is Johnson solid J_46.

			26.431335857944513546973871516071261950885787743598...

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

Cf. A385260 (volume).

Cf. A002163, A002194, A384284, A385257, A385259.

First[RealDigits[(20 + 15*Sqrt[3] + Sqrt[25 + 10*Sqrt[5]])/2, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J46", "SurfaceArea"], 10, 100]]

Equals (20 + 15*sqrt(3) + sqrt(25 + 10*sqrt(5)))/2 = (20 + 15*A002194 + sqrt(25 + 10*A002163))/2.

Equals the largest root of x^8 - 80*x^7 + 2100*x^6 - 14000*x^5 - 174750*x^4 + 1390000*x^3 + 9603125*x^2 + 9937500*x - 6546875.

A385509 Decimal expansion of the volume of an augmented pentagonal prism with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 01 2025

The augmented pentagonal prism is Johnson solid J_52.

			1.9561796609844827642259600980902259458356528159...

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

Cf. A385510 (surface area).

Cf. A002163.

First[RealDigits[Sqrt[233 + 90*Sqrt[5] + 12*Sqrt[50 + 20*Sqrt[5]]]/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J52", "Volume"], 10, 100]]

Equals sqrt(233 + 90*sqrt(5) + 12*sqrt(50 + 20*sqrt(5)))/12 = sqrt(233 + 90*A002163 + 12*sqrt(50 + 20*A002163))/12.

Equals the largest root of 429981696*x^8 - 2782937088*x^6 + 4776205824*x^4 - 1630792512*x^2 + 43414921.

A385695 Decimal expansion of the volume of an augmented dodecahedron with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 08 2025

The augmented dodecahedron is Johnson solid J_58.

			7.9646217930204565393997694898102032551644412276373...

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

Cf. A385696 (surface area).

Cf. A002163, A102769, A179552, A385802, A385804.

First[RealDigits[(95 + 43*Sqrt[5])/24, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J58", "Volume"], 10, 100]]

Equals (95 + 43*sqrt(5))/24 = (95 + 43*A002163)/24.
Equals A102769 + A179552.
Equals the largest root of 144*x^2 - 1140*x - 55.

A386000 Decimal expansion of the volume of a tridiminished icosahedron with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 14 2025

The tridiminished icosahedron is Johnson solid J_63.

			1.277186493437438661452675653379955568670180...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Tridiminished icosahedron.

Cf. A386001 (surfacea area).

Cf. A002163, A020829, A102208, A179552, A385857, A386002.

First[RealDigits[5/8 + 7*Sqrt[5]/24, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J63", "Volume"], 10, 100]]

Equals 5/8 + 7*sqrt(5)/24 = 5/8 + 7*A002163/24.
Equals A102208 - 3*A179552 = A386002 - A020829.
Equals the largest root of 144*x^2 - 180*x - 5.

A386002 Decimal expansion of the volume of an augmented tridiminished icosahedron with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 18 2025

The augmented tridiminished icosahedron is Johnson solid J_64.

			1.3950376236351965821861497137307637418843196778...

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

Cf. A386003 (surface area).

Cf. A002163, A010466, A020829, A102208, A179552, A385857, A386000.

First[RealDigits[(15 + Sqrt[8] + 7*Sqrt[5])/24, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J64", "Volume"], 10, 100]]

Equals (15 + 2*sqrt(2) + 7*sqrt(5))/24 = (15 + A010466 + 7*A002163)/24.
Equals A102208 - 3*A179552 + A020829 = A386000 + A020829.
Equals the largest root of 2304*x^4 - 5760*x^3 + 3376*x^2 + 280*x - 49.

A386466 Decimal expansion of the volume of a parabiaugmented truncated dodecahedron with unit edges.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jul 25 2025

The parabiaugmented truncated dodecahedron is Johnson solid J_69.

Also the volume of a metabiaugmented truncated dodecahedron (Johnson solid J_70) with unit edges.

			89.68775519603726781655854923762919459129960068854...

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

Cf. A386543 (surface area).

Cf. A002163, A179590, A377695, A385578, A385802, A386464, A386544.

First[RealDigits[(515 + 251*Sqrt[5])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J69", "Volume"], 10, 100]]

Equals (515 + 251*sqrt(5))/12 = (515 + 251*A002163)/12.
Equals A377695 + 2*A179590.
Equals the largest root of 36*x^2 - 3090*x - 12445.

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

Original entry on oeis.org

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.

A386689 Decimal expansion of the volume of a diminished rhombicosidodecahedron with unit edges.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jul 29 2025

The diminished rhombicosidodecahedron is Johnson solid J_76.

Also the volume of a paragyrate diminished rhombicosidodecahedron, a metagyrate diminished rhombicosidodecahedron and a bigyrate diminished rhombicosidodecahedron (Johnson solids J_77, J_78 and J_79, respectively) with unit edges.

			39.29127846416477393434922968524815278563223190317...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Wikipedia, Bigyrate diminished rhombicosidodecahedron.
Wikipedia, Diminished rhombicosidodecahedron.
Wikipedia, Metagyrate diminished rhombicosidodecahedron.
Wikipedia, Paragyrate diminished rhombicosidodecahedron.

Cf. A386690 (surface area).

Cf. A002163, A179590, A185093, A386691, A386693.

First[RealDigits[115/6 + 9*Sqrt[5], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J76", "Volume"], 10, 100]]

Equals 115/6 + 9*sqrt(5) = 115/6 + 9*A002163.
Equals A185093 - A179590.
Equals the largest root of 36*x^2 - 1380*x - 1355.

cp's OEIS Frontend

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

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A385260 Decimal expansion of the volume of a gyroelongated pentagonal bicupola with unit edge.

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A385261 Decimal expansion of the surface area of a gyroelongated pentagonal bicupola with unit edge.

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A385509 Decimal expansion of the volume of an augmented pentagonal prism with unit edge.

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A385695 Decimal expansion of the volume of an augmented dodecahedron with unit edge.

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A386000 Decimal expansion of the volume of a tridiminished icosahedron with unit edge.

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A386002 Decimal expansion of the volume of an augmented tridiminished icosahedron with unit edge.

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A386466 Decimal expansion of the volume of a parabiaugmented truncated dodecahedron with unit edges.

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