A378393 -id:A378393 - cp's OEIS frontend

A378712 Decimal expansion of the surface area of a disdyakis dodecahedron with unit shorter edge length.

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

Offset: 2

Paolo Xausa, Dec 06 2024

The disdyakis dodecahedron is the dual polyhedron of the truncated cuboctahedron (great rhombicuboctahedron).

			32.066734010531944413349823874895723462863495851553...

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

Cf. A378713 (volume), A378714 (inradius), A378393 (midradius), A378715 (dihedral angle).
Cf. A377343 (surface area of a truncated cuboctahedron (great rhombicuboctahedron) with unit edge length).
Cf. A002193.

First[RealDigits[6/7*Sqrt[783 + 436*Sqrt[2]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DisdyakisDodecahedron", "SurfaceArea"], 10, 100]]

sqrt(783 + 436*sqrt(2))*6/7 \\ Charles R Greathouse IV, Feb 05 2025

Equals (6/7)*sqrt(783 + 436*sqrt(2)) = (6/7)*sqrt(783 + 436*A002193).

A378713 Decimal expansion of the volume of a disdyakis dodecahedron with unit shorter edge length.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Dec 07 2024

The disdyakis dodecahedron is the dual polyhedron of the truncated cuboctahedron (great rhombicuboctahedron).

			16.288919082923525038503122503619441045996797447357...

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

Cf. A378712 (surface area), A378714 (inradius), A378393 (midradius), A378715 (dihedral angle).
Cf. A377344 (volume of a truncated cuboctahedron (great rhombicuboctahedron) with unit edge length).
Cf. A002193.

First[RealDigits[Sqrt[6582 + 4539*Sqrt[2]]/7, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DisdyakisDodecahedron", "Volume"], 10, 100]]

sqrt(3*(2194 + 1513*sqrt(2)))/7 \\ Charles R Greathouse IV, Feb 05 2025

Equals sqrt(3*(2194 + 1513*sqrt(2)))/7 = sqrt(6582 + 4539*A002193)/7.

A378714 Decimal expansion of the inradius of a disdyakis dodecahedron with unit shorter edge length.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Dec 07 2024

The disdyakis dodecahedron is the dual polyhedron of the truncated cuboctahedron (great rhombicuboctahedron).

			1.5239081483234575496935813294889545216581003925...

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

Cf. A378712 (surface area), A378713 (volume), A378393 (midradius), A378715 (dihedral angle).

Cf. A002193.

First[RealDigits[Sqrt[3/97*(166 + 95*Sqrt[2])]/2, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DisdyakisDodecahedron", "Inradius"], 10, 100]]

sqrt((166 + 95*sqrt(2))*3/97)/2 \\ Charles R Greathouse IV, Feb 05 2025

Equals sqrt((3/97)*(166 + 95*sqrt(2)))/2 = sqrt((3/97)*(166 + 95*A002193))/2.

A378715 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a disdyakis dodecahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Dec 07 2024

The disdyakis dodecahedron is the dual polyhedron of the truncated cuboctahedron (great rhombicuboctahedron).

			2.7066946454792287856258644383068280456984454555717...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Disdyakis dodecahedron.

Cf. A378712 (surface area), A378713 (volume), A378714 (inradius), A378393 (midradius).
Cf. A177870, A195698 and A195702 (dihedral angles of a truncated cuboctahedron (great rhombicuboctahedron)).
Cf. A002193.

First[RealDigits[ArcCos[-(71 + 12*Sqrt[2])/97], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["DisdyakisDodecahedron", "DihedralAngles"]], 10, 100]]

Equals arccos(-(71 + 12*sqrt(2))/97) = arccos(-(71 + 12*A002193)/97).

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)).

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).

A380734 Decimal expansion of the medium/short edge length ratio of a disdyakis dodecahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jan 31 2025

			1.33770871866841824565822846556337733622336049131...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Disdyakis Dodecahedron.
Wikipedia, Disdyakis dodecahedron.
Index entries for algebraic numbers, degree 2.

Cf. A380735 (long/short edge length ratio).

Cf. A010474, A378393, A378712, A378713, A378714, A378715, A380736, A380737, A380738.

First[RealDigits[3/14*(2 + 3*Sqrt[2]), 10, 100]]

(2 + 3*sqrt(2))*3/14 \\ Charles R Greathouse IV, Feb 05 2025

Equals (3/14)*(2 + 3*sqrt(2)) = (3/14)*(2 + A010474).

A380735 Decimal expansion of the long/short edge length ratio of a disdyakis dodecahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jan 31 2025

Apart from leading digits the same as A343069. - R. J. Mathar, Feb 03 2025

			1.630601937481870721257384103458528296938524553625...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Disdyakis Dodecahedron.
Wikipedia, Disdyakis dodecahedron.
Index entries for algebraic numbers, degree 2.

Cf. A380734 (medium/short edge length ratio).

Cf. A002193, A378393, A378712, A378713, A378714, A378715, A380736, A380737, A380738.

First[RealDigits[(10 + Sqrt[2])/7, 10, 100]]

(10 + sqrt(2))/7 \\ Charles R Greathouse IV, Feb 05 2025

Equals (10 + sqrt(2))/7 = (10 + A002193)/7.

cp's OEIS Frontend

A378712 Decimal expansion of the surface area of a disdyakis dodecahedron with unit shorter edge length.

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A378713 Decimal expansion of the volume of a disdyakis dodecahedron with unit shorter edge length.

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A378714 Decimal expansion of the inradius of a disdyakis dodecahedron with unit shorter edge length.

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A378715 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a disdyakis dodecahedron.

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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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