A377995 -id:A377995 - cp's OEIS frontend

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

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).

A379389 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a deltoidal hexecontahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Dec 23 2024

The deltoidal hexecontahedron is the dual polyhedron of the (small) rhombicosidodecahedron.

			2.6899252342065763400728815146316168300353303724921...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Deltoidal Hexecontahedron.
Wikipedia, Deltoidal hexecontahedron.

Cf. A379385 (surface area), A379386 (volume), A379387 (inradius), A379388 (midradius).
Cf. A377995 and A377996 (dihedral angles of a (small) rhombicosidodecahedron).
Cf. A002163.

First[RealDigits[ArcCos[-(19 + 8*Sqrt[5])/41], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["DeltoidalHexecontahedron", "DihedralAngles"]], 10, 100]]

Equals arccos(-(19 + 8*sqrt(5))/41) = arccos(-(19 + 8*A002163)/41).

A377996 Decimal expansion of the dihedral angle, in radians, between triangular and square faces in a (small) rhombicosidodecahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Nov 15 2024

Also the dihedral angle, in radians, between square and hexagonal faces in a truncated icosidodecahedron (great rhombicosidodecahedron).

			2.7767288254763100567352450533728425364989164423512...

Eric Weisstein's World of Mathematics, Great Rhombicosidodecahedron.
Eric Weisstein's World of Mathematics, Small Rhombicosidodecahedron.

Cf. A002194, A010472, A377995.

First[RealDigits[ArcCos[-(Sqrt[3] + Sqrt[15])/6], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["Rhombicosidodecahedron", "DihedralAngles"]], 10, 100]]

Equals arccos(-(sqrt(3) + sqrt(15))/6) = arccos(-(A002194 + A010472)/6).

A387189 Decimal expansion of the smallest dihedral angle, in radians, in a pentagonal bipyramid (Johnson solid J_13).

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 21 2025

This is the dihedral angle between triangular faces at the edge where the two pyramidal parts of the solid meet.

Also the dihedral angle between triangular faces in a pentagonal orthobicupola (Johnson solid J_30).

			1.3047162795687363719907812632876451487306158399...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Pentagonal bipyramid.
Wikipedia, Pentagonal orthobicupola.

Cf. A236367 (J_13 smallest dihedral angle).
Cf. other J_30 dihedral angles: A105199, A377995, A377996.
Cf. A179641 (J_13 volume), A120011 (J_13 surface area, divided by 10).
Cf. A384624 (J_30 volume), A384625 (J_30 surface area).
Cf. A010532, A386852.

First[RealDigits[ArcCos[(Sqrt[80] - 5)/15], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J13", "DihedralAngles"]], 10, 100]]

Equals arccos((4*sqrt(5) - 5)/15) = arccos((A010532 - 5)/15).

Equals 2*A386852.

A387190 Decimal expansion of the second smallest dihedral angle, in radians, in an elongated pentagonal cupola (Johnson solid J_20).

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 22 2025

This is the dihedral angle between adjacent square faces at the edge where the prism and cupola parts of the solid meet.
Also the analogous dihedral angle in Johnson solids J_38-J_41.
Also the dihedral angle between a square face and a decagonal face in Johnson solids J_76-J_83.

			2.124370685691941870739854421729019962133608522388...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Elongated pentagonal cupola.

Cf. other J_20 dihedral angles: A019669, A228824, A377995, A377996, A387147.
Cf. A384144 (J_20 volume), A179591 (J_20 surface area - 10).
Cf. A002163.

First[RealDigits[ArcCos[-Sqrt[(5 - Sqrt[5])/10]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J20", "DihedralAngles"]], 2], 10, 100]]

Equals arccos(-sqrt((5 - sqrt(5))/10)) = arccos(-sqrt((5 - A002163)/10)).

cp's OEIS Frontend

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

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A379389 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a deltoidal hexecontahedron.

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A377996 Decimal expansion of the dihedral angle, in radians, between triangular and square faces in a (small) rhombicosidodecahedron.

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A387189 Decimal expansion of the smallest dihedral angle, in radians, in a pentagonal bipyramid (Johnson solid J_13).

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A387190 Decimal expansion of the second smallest dihedral angle, in radians, in an elongated pentagonal cupola (Johnson solid J_20).

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