A378712 -id:A378712 - cp's OEIS frontend

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

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).

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.

A380736 Decimal expansion of the smallest vertex angle, in radians, in a disdyakis dodecahedron face.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Feb 01 2025

A disdyakis dodecahedron face is a scalene triangle with three acute angles.

			0.6592691539262158395617269590815416456187802510390...

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

Cf. A380737 (face medium angle), A380738 (face largest angle).

Cf. A010503, A378393, A378712, A378713, A378714, A378715, A380734, A380735.

First[RealDigits[ArcCos[1/12 + Sqrt[2]/2], 10, 100]]

Equals arccos(1/12 + sqrt(2)/2) = arccos(1/12 + A010503).

Equals Pi - A380737 - A380738.

A380737 Decimal expansion of the medium vertex angle, in radians, in a disdyakis dodecahedron face.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Feb 01 2025

A disdyakis dodecahedron face is a scalene triangle with three acute angles.

			0.96036211770779573574013915231457685647777081770813...

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

Cf. A380736 (face smallest angle), A380738 (face largest angle).

Cf. A020789, A378393, A378712, A378713, A378714, A378715, A380734, A380735.

First[RealDigits[ArcCos[3/4 - Sqrt[2]/8], 10, 100]]

Equals arccos(3/4 - sqrt(2)/8) = arccos(3/4 - A020789).

Equals Pi - A380736 - A380738.

A380738 Decimal expansion of the largest vertex angle, in radians, in a disdyakis dodecahedron face.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Feb 01 2025

A disdyakis dodecahedron face is a scalene triangle with three acute angles.

			1.5219613819557816631607772718833843821006183306...

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

Cf. A380736 (face smallest angle), A380737 (face medium angle).

Cf. A020829, A378393, A378712, A378713, A378714, A378715, A380734, A380735.

First[RealDigits[ArcCos[1/6 - Sqrt[2]/12], 10, 100]]

Equals arccos(1/6 - sqrt(2)/12) = arccos(1/6 - A020829).

Equals Pi - A380736 - A380737.

A382006 Decimal expansion of the isoperimetric quotient of a disdyakis dodecahedron.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Mar 18 2025

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

			0.91006563880803117059123808570537149844558354540595...

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

Cf. A378712 (surface area), A378713 (volume).

Cf. A000796, A002193, A381684.

First[RealDigits[Pi*7/97*Sqrt[(1709 + 1002*Sqrt[2])/194], 10, 100]]

Equals 36*Pi*A378713^2/(A378712^3).

Equals (Pi*7/97)*sqrt((1709 + 1002*sqrt(2))/194) = (A000796*7/97)*sqrt((1709 + 1002*A002193)/194).

cp's OEIS Frontend

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

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

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A380736 Decimal expansion of the smallest vertex angle, in radians, in a disdyakis dodecahedron face.

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A380737 Decimal expansion of the medium vertex angle, in radians, in a disdyakis dodecahedron face.

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