A378393 -id:A378393 - cp's OEIS frontend

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

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.

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

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

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Mathematica

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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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