A386740 -id:A386740 - cp's OEIS frontend

A386741 Decimal expansion of the volume of a hebesphenomegacorona with unit edges.

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

Offset: 1

Paolo Xausa, Aug 01 2025

The hebesphenomegacorona is Johnson solid J_89.

			2.912910414540209166042800910083320363836153037751...

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

Cf. A386742 (surface area).

Cf. A386739, A386740.

First[RealDigits[Root[47330370277129322496*#^20 - 722445512980071186432*#^18 + 3596480447590271287296*#^16 - 8432333285523990773760*#^14 + 8973584611317745975296*#^12 - 3065290664181478981632*#^10 + 366229890219212144640*#^8 - 8337259437908852736*#^6 - 22211277300912896*#^4 + 132615435213216*#^2 + 2693461945329 &, 8], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J89", "Volume"], 10, 100]]

Equals the largest real root of 47330370277129322496*x^20 - 722445512980071186432*x^18 + 3596480447590271287296*x^16 - 8432333285523990773760*x^14 + 8973584611317745975296*x^12 - 3065290664181478981632*x^10 + 366229890219212144640*x^8 - 8337259437908852736*x^6 - 22211277300912896*x^4 + 132615435213216*x^2 + 2693461945329.

A386739 Decimal expansion of the volume of a sphenocorona with unit edges.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 01 2025

The sphenocorona is Johnson solid J_86.

			1.5153516399764065597284793124718129048228695068...

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

Cf. A010482 (surface area - 2), A178809 (surface area + 4).

Cf. A010507, A020775, A115754, A386740, A386741.

First[RealDigits[Sqrt[1 + 3*Sqrt[3/2] + Sqrt[13 + Sqrt[54]]]/2, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J86", "Volume"], 10, 100]]

Equals sqrt(1 + 3*sqrt(3/2) + sqrt(13 + 3*sqrt(6)))/2 = sqrt(1 + 3*A115754  + sqrt(13 + A010507))/2.
Equals A386740 - A020775.
Equals the largest real root of 1024*x^8 - 1024*x^6 - 3008*x^4 - 96*x^2 + 9.

cp's OEIS Frontend

A386741 Decimal expansion of the volume of a hebesphenomegacorona with unit edges.

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