A379708 -id:A379708 - cp's OEIS frontend

A379709 Decimal expansion of the volume of a disdyakis triacontahedron with unit shorter edge length.

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

Offset: 2

Paolo Xausa, Dec 31 2024

The disdyakis triacontahedron is the dual polyhedron of the truncated icosidodecahedron (great rhombicosidodecahedron).

			84.1819754400481313518959942929339817444032991207...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.
Wikipedia, Disdyakis triacontahedron.

Cf. A379708 (surface area), A379710 (inradius), A379388 (midradius), A379711 (dihedral angle).
Cf. A377797 (volume of a truncated icosidodecahedron (great rhombicosidodecahedron) with unit edge length).
Cf. A002163.

First[RealDigits[Sqrt[88590 + 39612*Sqrt[5]]/5, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DisdyakisTriacontahedron", "Volume"], 10, 100]]

Equals sqrt(88590 + 39612*sqrt(5))/5 = sqrt(88590 + 39612*A002163)/5.

A379710 Decimal expansion of the inradius of a disdyakis triacontahedron with unit shorter edge length.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Dec 31 2024

The disdyakis triacontahedron is the dual polyhedron of the truncated icosidodecahedron (great rhombicosidodecahedron).

			2.679969340204835578579553327459806767085423038168...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.
Wikipedia, Disdyakis triacontahedron.

Cf. A379708 (surface area), A379709 (volume), A379388 (midradius), A379711 (dihedral angle).

Cf. A002163.

First[RealDigits[Sqrt[3477/964 + 7707/(964*Sqrt[5])], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DisdyakisTriacontahedron", "Inradius"], 10, 100]]

Equals sqrt(3477/964 + 7707/(964*sqrt(5))) = sqrt(3477/964 + 7707/(964*A002163)).

A379711 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a disdyakis triacontahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Dec 31 2024

The disdyakis triacontahedron is the dual polyhedron of the truncated icosidodecahedron (great rhombicosidodecahedron).

			2.8778366104612242809434504548179917754749428665406...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.
Wikipedia, Disdyakis triacontahedron.

Cf. A379708 (surface area), A379709 (volume), A379710 (inradius), A379388 (midradius).
Cf. A344075, A377995 and A377996 (dihedral angles of a truncated icosidodecahedron (great rhombicosidodecahedron)).
Cf. A002163.

First[RealDigits[ArcCos[(-179 - 24*Sqrt[5])/241], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["DisdyakisTriacontahedron", "DihedralAngles"]], 10, 100]]

Equals arccos((-179 - 24*sqrt(5))/241) = arccos((-179 - 24*A002163)/241).

A380940 Decimal expansion of the smallest vertex angle, in radians, in a disdyakis triacontahedron face.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Feb 08 2025

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

			0.57194925611938685598415462715533824150730405467310...

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

Cf. A380941 (middle face angle), A380942 (face largest face angle).

Cf. A001622, A379388, A379708, A379709, A379710, A379711.

First[RealDigits[ArcCos[(2 + 5*GoldenRatio)/12], 10, 100]]

Equals arccos((2 + 5*A001622)/12).

Equals Pi - A380941 - A380942.

A380941 Decimal expansion of the middle vertex angle, in radians, in a disdyakis triacontahedron face.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Feb 08 2025

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

			1.016443446896330150160097551517069643637928892906...

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

Cf. A380940 (smallest face angle), A380942 (largest face angle).

Cf. A001622, A379388, A379708, A379709, A379710, A379711.

First[RealDigits[ArcCos[(17 - 4*GoldenRatio)/20], 10, 100]]

Equals arccos((17 - 4*A001622)/20).

Equals Pi - A380940 - A380942.

A380942 Decimal expansion of the largest vertex angle, in radians, in a disdyakis triacontahedron face.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Feb 09 2025

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

			1.5531999505740762323183912046070949990519364517956...

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

Cf. A380940 (smallest face angle), A380941 (middle face angle).

Cf. A001622, A379388, A379708, A379709, A379710, A379711.

First[RealDigits[ArcCos[(7 - 4*GoldenRatio)/30], 10, 100]]

Equals arccos((7 - 4*A001622)/30).

Equals Pi - A380940 - A380941.

A380981 Decimal expansion of the medium/short edge length ratio of a disdyakis triacontahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Feb 10 2025

			1.57082039324993690892275210061938287063218550788...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.
Wikipedia, Disdyakis triacontahedron.

Cf. A380982 (long/short edge length ratio).
Cf. A002163, A379388, A379708, A379709, A379710, A379711, A380940, A380941, A380942.
Apart from leading digits the same as A176015, A134976 and A010499.

First[RealDigits[3/10*(3 + Sqrt[5]), 10, 100]]

Equals (3/10)*(3 + sqrt(5)) = (3/10)*(3 + A002163).

Equals A176015 + 2/5.

A380982 Decimal expansion of the long/short edge length ratio of a disdyakis triacontahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Feb 10 2025

			1.8472135954999579392818347337462552470881236719223...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.
Wikipedia, Disdyakis triacontahedron.

Cf. A380981 (medium/short edge length ratio).
Cf. A020762, A379388, A379708, A379709, A379710, A379711, A380940, A380941, A380942.
Apart from leading digits the same as A176453, A134974 and A010476.

First[RealDigits[7/5 + 1/Sqrt[5], 10, 100]] (* Paolo Xausa, Feb 10 2025 *)

Equals 1/sqrt(5) + 7/5 = A020762 + 7/5.

A382012 Decimal expansion of the isoperimetric quotient of a disdyakis triacontahedron.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Mar 20 2025

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

The disdyakis triacontahedron is the Catalan solid with the highest isoperimetric quotient.

			0.95776502384780769076187408953240617790783343820517...

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

Cf. A379708 (surface area), A379709 (volume).

Cf. A000796, A381684.

First[RealDigits[Pi*Root[13997521*#^4 - 1302278*#^2 + 121 &, 4], 10, 100]]

Equals 36*Pi*A379709^2/(A379708^3).

Equals Pi*r = A000796*r, where r is the largest root of 13997521*x^4 - 1302278*x^2 + 121.

cp's OEIS Frontend

A379709 Decimal expansion of the volume of a disdyakis triacontahedron with unit shorter edge length.

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A379710 Decimal expansion of the inradius of a disdyakis triacontahedron with unit shorter edge length.

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A379711 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a disdyakis triacontahedron.

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A380940 Decimal expansion of the smallest vertex angle, in radians, in a disdyakis triacontahedron face.

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A380941 Decimal expansion of the middle vertex angle, in radians, in a disdyakis triacontahedron face.

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A380942 Decimal expansion of the largest vertex angle, in radians, in a disdyakis triacontahedron face.

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A380981 Decimal expansion of the medium/short edge length ratio of a disdyakis triacontahedron.

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A380982 Decimal expansion of the long/short edge length ratio of a disdyakis triacontahedron.

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