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Search: a379710 -id:a379710
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A379708
Decimal expansion of the surface area of a disdyakis triacontahedron with unit shorter edge length.
+10
9
9, 4, 2, 3, 4, 6, 3, 2, 6, 6, 2, 1, 9, 3, 7, 3, 5, 6, 0, 1, 5, 0, 3, 5, 0, 6, 5, 2, 0, 5, 4, 9, 1, 5, 9, 8, 7, 4, 9, 9, 7, 3, 1, 0, 4, 5, 3, 7, 0, 8, 1, 3, 1, 2, 1, 3, 8, 8, 6, 9, 4, 7, 9, 2, 6, 1, 9, 5, 9, 3, 1, 5, 5, 2, 8, 1, 8, 5, 8, 9, 0, 6, 7, 9, 3, 6, 7, 1, 2, 5
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
The disdyakis triacontahedron is the dual polyhedron of the truncated icosidodecahedron (great rhombicosidodecahedron).
LINKS
Paolo Xausa, Table of n, a(n) for n = 2..10000
Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.
Wikipedia, Disdyakis triacontahedron.
FORMULA
Equals sqrt(22626/5 + 9738/sqrt(5)) = sqrt(22626/5 + 9738/A002163).
EXAMPLE
94.234632662193735601503506520549159874997310453708...
MATHEMATICA
First[RealDigits[Sqrt[22626/5 + 9738/Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DisdyakisTriacontahedron", "SurfaceArea"], 10, 100]]
CROSSREFS
Cf. A379709 (volume), A379710 (inradius), A379388 (midradius), A379711 (dihedral angle).
Cf. A377796 (surface area of a truncated icosidodecahedron (great rhombicosidodecahedron) with unit edge length).
Cf. A002163.
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Dec 31 2024
STATUS
approved
A379709
Decimal expansion of the volume of a disdyakis triacontahedron with unit shorter edge length.
+10
9
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
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
The disdyakis triacontahedron is the dual polyhedron of the truncated icosidodecahedron (great rhombicosidodecahedron).
LINKS
Paolo Xausa, Table of n, a(n) for n = 2..10000
Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.
Wikipedia, Disdyakis triacontahedron.
FORMULA
Equals sqrt(88590 + 39612*sqrt(5))/5 = sqrt(88590 + 39612*A002163)/5.
EXAMPLE
84.1819754400481313518959942929339817444032991207...
MATHEMATICA
First[RealDigits[Sqrt[88590 + 39612*Sqrt[5]]/5, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DisdyakisTriacontahedron", "Volume"], 10, 100]]
CROSSREFS
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.
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Dec 31 2024
STATUS
approved
A379711
Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a disdyakis triacontahedron.
+10
9
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
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The disdyakis triacontahedron is the dual polyhedron of the truncated icosidodecahedron (great rhombicosidodecahedron).
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.
Wikipedia, Disdyakis triacontahedron.
FORMULA
Equals arccos((-179 - 24*sqrt(5))/241) = arccos((-179 - 24*A002163)/241).
EXAMPLE
2.8778366104612242809434504548179917754749428665406...
MATHEMATICA
First[RealDigits[ArcCos[(-179 - 24*Sqrt[5])/241], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["DisdyakisTriacontahedron", "DihedralAngles"]], 10, 100]]
CROSSREFS
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.
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Dec 31 2024
STATUS
approved
A380940
Decimal expansion of the smallest vertex angle, in radians, in a disdyakis triacontahedron face.
+10
5
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
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
A disdyakis triacontahedron face is a scalene triangle with three acute angles.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..10000
Wikipedia, Disdyakis triacontahedron.
FORMULA
Equals arccos((2 + 5*A001622)/12).
Equals Pi - A380941 - A380942.
EXAMPLE
0.57194925611938685598415462715533824150730405467310...
MATHEMATICA
First[RealDigits[ArcCos[(2 + 5*GoldenRatio)/12], 10, 100]]
CROSSREFS
Cf. A380941 (middle face angle), A380942 (face largest face angle).
Cf. A001622, A379388, A379708, A379709, A379710, A379711.
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Feb 08 2025
STATUS
approved
A380941
Decimal expansion of the middle vertex angle, in radians, in a disdyakis triacontahedron face.
+10
5
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
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
A disdyakis triacontahedron face is a scalene triangle with three acute angles.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Disdyakis triacontahedron.
FORMULA
Equals arccos((17 - 4*A001622)/20).
Equals Pi - A380940 - A380942.
EXAMPLE
1.016443446896330150160097551517069643637928892906...
MATHEMATICA
First[RealDigits[ArcCos[(17 - 4*GoldenRatio)/20], 10, 100]]
CROSSREFS
Cf. A380940 (smallest face angle), A380942 (largest face angle).
Cf. A001622, A379388, A379708, A379709, A379710, A379711.
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Feb 08 2025
STATUS
approved
A380942
Decimal expansion of the largest vertex angle, in radians, in a disdyakis triacontahedron face.
+10
5
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
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A disdyakis triacontahedron face is a scalene triangle with three acute angles.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Disdyakis triacontahedron.
FORMULA
Equals arccos((7 - 4*A001622)/30).
Equals Pi - A380940 - A380941.
EXAMPLE
1.5531999505740762323183912046070949990519364517956...
MATHEMATICA
First[RealDigits[ArcCos[(7 - 4*GoldenRatio)/30], 10, 100]]
CROSSREFS
Cf. A380940 (smallest face angle), A380941 (middle face angle).
Cf. A001622, A379388, A379708, A379709, A379710, A379711.
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Feb 09 2025
STATUS
approved
A380981
Decimal expansion of the medium/short edge length ratio of a disdyakis triacontahedron.
+10
2
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
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.
Wikipedia, Disdyakis triacontahedron.
FORMULA
Equals (3/10)*(3 + sqrt(5)) = (3/10)*(3 + A002163).
Equals A176015 + 2/5.
EXAMPLE
1.57082039324993690892275210061938287063218550788...
MATHEMATICA
First[RealDigits[3/10*(3 + Sqrt[5]), 10, 100]]
CROSSREFS
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.
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Feb 10 2025
STATUS
approved
A380982
Decimal expansion of the long/short edge length ratio of a disdyakis triacontahedron.
+10
2
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
(list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Disdyakis Triacontahedron.
Wikipedia, Disdyakis triacontahedron.
FORMULA
Equals 1/sqrt(5) + 7/5 = A020762 + 7/5.
EXAMPLE
1.8472135954999579392818347337462552470881236719223...
MATHEMATICA
First[RealDigits[7/5 + 1/Sqrt[5], 10, 100]] (* Paolo Xausa, Feb 10 2025 *)
CROSSREFS
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.
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Feb 10 2025
STATUS
approved
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