A378394 -id:A378394 - cp's OEIS frontend

A378393 Decimal expansion of the midradius of a deltoidal icositetrahedron with unit shorter edge length.

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

Offset: 1

Paolo Xausa, Nov 30 2024

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

			1.5606601717798212866012665431572735589272539065327...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Index entries for algebraic numbers, degree 2.

Cf. A378390 (surface area), A378391 (volume), A378392 (inradius), A378394 (dihedral angle).
Cf. A285871 (midradius of a (small) rhombicuboctahedron with unit edge).
Cf. A010474, A093577.

First[RealDigits[(2 + Sqrt[18])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DeltoidalIcositetrahedron", "Midradius"], 10, 100]]

Equals (2 + 3*sqrt(2))/4 = (2 + A010474)/4.

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

Original entry on oeis.org

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).

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

Original entry on oeis.org

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).

A378392 Decimal expansion of the inradius of a deltoidal icositetrahedron with unit shorter edge length.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Nov 30 2024

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

			1.4575767431694506679193428707184970573873139019359...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Index entries for algebraic numbers, degree 4.

Cf. A378390 (surface area), A378391 (volume), A378393 (midradius), A378394 (dihedral angle).

Cf. A002193.

First[RealDigits[Sqrt[39/34 + 47/(34*Sqrt[2])], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DeltoidalIcositetrahedron", "Inradius"], 10, 100]]

Equals sqrt(39/34 + 47/(34*sqrt(2))) = sqrt(39/34 + 47/(34*A002193)).

A380704 Decimal expansion of the acute vertex angles, in radians, in a deltoidal icositetrahedron face.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jan 31 2025

			1.4238211361313915494455573566669046848857979902951...

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

Cf. A380705 (obtuse face angle).

Cf. A020765, A378390, A378391, A378392, A378393, A378394.

First[RealDigits[ArcCos[1/2 - Sqrt[2]/4], 10, 100]]

Equals arccos(1/2 - sqrt(2)/4) = arccos(1/2 - A020765).

Equals (2*Pi - A380705)/3.

A380705 Decimal expansion of the obtuse vertex angle, in radians, in a deltoidal icositetrahedron face.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jan 31 2025

			2.0117218987854118285886146965582917137369448278649...

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

Cf. A380704 (face acute angles).

Cf. A020789, A378390, A378391, A378392, A378393, A378394.

First[RealDigits[ArcCos[-1/4 - Sqrt[2]/8], 10, 100]]

Equals arccos(-1/4 - sqrt(2)/8) = arccos(-1/4 - A020789).

Equals 2*Pi - 3*A380704.

cp's OEIS Frontend

A378393 Decimal expansion of the midradius of a deltoidal icositetrahedron with unit shorter edge length.

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

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

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A378392 Decimal expansion of the inradius of a deltoidal icositetrahedron with unit shorter edge length.

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A380704 Decimal expansion of the acute vertex angles, in radians, in a deltoidal icositetrahedron face.

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A380705 Decimal expansion of the obtuse vertex angle, in radians, in a deltoidal icositetrahedron face.

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