A378391 -id:A378391 - 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).

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)).

A378394 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a deltoidal icositetrahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Nov 30 2024

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

			2.410613141653407606153665785465949185980362906...

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

Cf. A378390 (surface area), A378391 (volume), A378392 (inradius), A378393 (midradius).

Cf. A177870 and A195702 (dihedral angles of a (small) rhombicuboctahedron).

First[RealDigits[ArcSec[Sqrt[32] - 7], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["DeltoidalIcositetrahedron", "DihedralAngles"]], 10, 100]]

acos(-(4*sqrt(2) + 7)/17) \\ Charles R Greathouse IV, Feb 11 2025

Equals arcsec(4*sqrt(2) - 7) = arcsec(A010487 - 7).

Equals arccos(-(4*sqrt(2) + 7)/17) = arccos(-(A010487 + 7)/17).

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.

A382005 Decimal expansion of the isoperimetric quotient of a deltoidal icositetrahedron.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Mar 17 2025

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

			0.8697742819100637602738942626812998578199050663867...

Paolo Xausa, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers

Cf. A378390 (surface area), A378391 (volume).

Cf. A000796, A002193, A381684.

First[RealDigits[Pi/51*Sqrt[(3407 + 2384*Sqrt[2])/34], 10, 100]]

Equals 36*Pi*A378391^2/(A378390^3).

Equals (Pi/51)*sqrt((3407 + 2384*sqrt(2))/34) = (A000796/51)*sqrt((3407 + 2384*A002193)/34).

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A378394 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a deltoidal icositetrahedron.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A382005 Decimal expansion of the isoperimetric quotient of a deltoidal icositetrahedron.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula