A343965 -id:A343965 - cp's OEIS frontend

A378391 Decimal expansion of the volume of a deltoidal icositetrahedron with unit shorter edge length.

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

Offset: 2

Paolo Xausa, Nov 30 2024

The deltoidal icositetrahedron is the dual polyhedron of the (small) rhombicuboctahedron.

			14.9133887137863387908227981130654481094824451352...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Eric Weisstein's World of Mathematics, Deltoidal Icositetrahedron.
Wikipedia, Deltoidal icositetrahedron.
Index entries for algebraic numbers, degree 4.

Cf. A378390 (surface area), A378392 (inradius), A378393 (midradius), A378394 (dihedral angle).
Cf. A343965 (volume of a (small) rhombicuboctahedron with unit edge).
Cf. A002193.

First[RealDigits[Sqrt[122 + 71*Sqrt[2]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DeltoidalIcositetrahedron", "Volume"], 10, 100]]

Equals sqrt(122 + 71*sqrt(2)) = sqrt(122 + 71*A002193).

A343964 Decimal expansion of 18 + 2*sqrt(3).

Original entry on oeis.org

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

Offset: 1

Wesley Ivan Hurt, May 05 2021

Surface area of a rhombicuboctahedron with unit edge length.

Essentially the same sequence of digits as A176394 and A010469. - R. J. Mathar, May 07 2021

			21.464101615137754587054892683011744733885...

Wikipedia, Rhombicuboctahedron

Cf. A343965 (rhombicuboctahedron volume).

SetDefaultRealField(RealField(100)); 18+2*Sqrt(3);

RealDigits[N[18 + 2*Sqrt[3], 100]][[1]] (* Wesley Ivan Hurt, Nov 12 2022 *)

A381688 Decimal expansion of the isoperimetric quotient of a (small) rhombicuboctahedron.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Mar 04 2025

For the definition of isoperimetric quotient of a solid, references and links, see A381684.

			0.8684680457998683969444644014889968511341210788731...

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A343964 (surface area), A343965 (volume).

Cf. A000796, A002193, A002194, A381684.

First[RealDigits[4*Pi*(43 + 30*Sqrt[2])/(9 + Sqrt[3])^3, 10, 100]]

Equals 36*Pi*A343965^2/(A343964^3).

Equals 4*Pi*(43 + 30*sqrt(2))/((9 + sqrt(3))^3) = 4*A000796*(43 + 30*A002193)/((9 + A002194)^3).

A343966 Decimal expansion of (4/3)(4sqrt(2)-5).

Original entry on oeis.org

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

Offset: 0

Wesley Ivan Hurt, May 05 2021

The optimal packing fraction of a rhombicuboctahedron is (4/3)*(4*sqrt(2)-5).

			0.87580566598984026027567319578505641903825...

Wikipedia, Rhombicuboctahedron

Cf. A343964 (rhombicuboctahedron surface area).

Cf. A343965 (rhombicuboctahedron volume).

SetDefaultRealField(RealField(100)); (4/3)*(4*Sqrt(2)-5);

RealDigits[N[(4/3)*(4*Sqrt[2] - 5), 100]][[1]] (* Wesley Ivan Hurt, Nov 12 2022 *)

cp's OEIS Frontend

A378391 Decimal expansion of the volume of a deltoidal icositetrahedron with unit shorter edge length.

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A343964 Decimal expansion of 18 + 2*sqrt(3).

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A381688 Decimal expansion of the isoperimetric quotient of a (small) rhombicuboctahedron.

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A343966 Decimal expansion of (4/3)*(4*sqrt(2)-5).

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A343966 Decimal expansion of (4/3)(4sqrt(2)-5).