A343964 -id:A343964 - cp's OEIS frontend

A378390 Decimal expansion of the surface area of a deltoidal icositetrahedron with unit shorter edge length.

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

Offset: 2

Paolo Xausa, Nov 29 2024

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

			30.694895724031009590770314784050673387965107463161...

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. A378391 (volume), A378392 (inradius), A378393 (midradius), A378394 (dihedral angle).
Cf. A343964 (surface area of a (small) rhombicuboctahedron with unit edge).
Cf. A010466.

First[RealDigits[6*Sqrt[29 - Sqrt[8]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DeltoidalIcositetrahedron", "SurfaceArea"], 10, 100]]

Equals 6*sqrt(29 - 2*sqrt(2)) = 6*sqrt(29 - A010466).

A343965 Decimal expansion of 4 + 10*sqrt(2)/3.

Original entry on oeis.org

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

Offset: 1

Wesley Ivan Hurt, May 05 2021

Volume of a rhombicuboctahedron with unit edge length.

Apart from the leading digit and offset the same as A131594. - R. J. Mathar, May 07 2021

			8.7140452079103168293389624140323269285655729...

Wikipedia, Rhombicuboctahedron

Cf. A343964 (rhombicuboctahedron surface area).

SetDefaultRealField(RealField(100)); 4+10*Sqrt(2)/3;

RealDigits[N[4 + 10*Sqrt[2]/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

A378390 Decimal expansion of the surface area of a deltoidal icositetrahedron with unit shorter edge length.

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A343965 Decimal expansion of 4 + 10*sqrt(2)/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).