A386739 -id:A386739 - 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.

A386740 Decimal expansion of the volume of an augmented sphenocorona with unit edges.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 01 2025

The augmented sphenocorona is Johnson solid J_87.

			1.7510539003719224011954274331734292512511481527...

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

Cf. A010502 (surface area - 1).

Cf. A010507, A020775, A115754, A386739, A386741.

First[RealDigits[Sqrt[1 + 3*Sqrt[3/2] + Sqrt[13 + Sqrt[54]]]/2 + 1/Sqrt[18], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J87", "Volume"], 10, 100]]

Equals sqrt(1 + 3*sqrt(3/2) + sqrt(13 + 3*sqrt(6)))/2 + 1/(3*sqrt(2)) = sqrt(1 + 3*A115754  + sqrt(13 + A010507))/2 + A020775.
Equals A386739 + A020775.
Equals the largest real root of 45137758519296*x^16 - 110336743047168*x^14 - 191069246324736*x^12 + 209269081571328*x^10 + 364547659290624*x^8 - 58793017190400*x^6 + 3306865979520*x^4 - 1275399855936*x^2 + 1439671249.

cp's OEIS Frontend

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

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