A384214 Decimal expansion of the volume of a gyroelongated square cupola with unit edge.

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

Offset: 1

Author

Paolo Xausa, May 23 2025

Keywords

• nonn
• cons
• easy

Comments

The gyroelongated square cupola is Johnson solid J_23.

Examples

			6.21076579203920003665822883345980731696010032091...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Gyroelongated square cupola.

Crossrefs

Cf. A384215 (surface area).

Cf. A002193, A010466, A179587, A179638, A384142.

Programs

Mathematica

First[RealDigits[1 + Sqrt[8]/3 + 2/3*Sqrt[4 + Sqrt[8] + 2*Sqrt[146 + 103*Sqrt[2]]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J23", "Volume"], 10, 100]]

Formula

Equals 1 + (2/3)*sqrt(2) + (2/3)*sqrt(4 + 2*sqrt(2) + 2*sqrt(146 + 103*sqrt(2))) = 1 + A010466/3 + (2/3)*sqrt(4 + A010466 + 2*sqrt(146 + 103*A002193)).

Equals the largest real root of 6561*x^8 - 52488*x^7 + 113724*x^6 - 9720*x^5 - 1616922*x^4 + 396360*x^3 + 1537020*x^2 - 178632*x - 3391.