A179552 -id:A179552 - cp's OEIS frontend

A386852 Decimal expansion of the dihedral angle, in radians, between the pentagonal face and a triangular face in a pentagonal pyramid with equal edges (Johnson solid J_2).

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

Offset: 0

Paolo Xausa, Aug 05 2025

Also the dihedral angle, in radians, between the 10-gonal face and a triangular face in a pentagonal cupola (Johnson solid J_5)

			0.65235813978436818599539063164382257436530791996...

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

Cf. A179552 (J_2 volume), A179553 (J_2 surface area).
Cf. A179590 (J_5 volume), A179591 (J_5 surface area).
Cf. A002163, A010476.

First[RealDigits[ArcSec[Sqrt[15 - 6*Sqrt[5]]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J2", "DihedralAngles"]], 10, 100]]

acos(sqrt((5+2*sqrt(5))/15)) \\ Charles R Greathouse IV, Aug 19 2025

Equals arcsec(sqrt(15 - 6*sqrt(5))) = arcsec(sqrt(15 - 6*A002163)).

Equals arccos(sqrt((5 + 2*sqrt(5))/15)) = arccos(sqrt((5 + A010476)/15)).

A334114 Decimal expansion of volume of a sphenomegacorona (J88) with each edge of unit length.

Original entry on oeis.org

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

Offset: 1

Violeta Hernández Palacios, Apr 14 2020

A sphenomegacorona is one of the 92 regular-faced non-isogonal convex polyhedra first enumerated by Norman W. Johnson. It's built out of 2 squares and 12 equilateral triangles.
This number is algebraic, of unknown degree.
It appears that the minimal polynomial is 521578814501447328359509917696*x^32 - 985204427391622731345740955648*x^30 - 16645447351681991898880656015360*x^28 + 79710816694053483249372512649216*x^26 - 152195045391070538203422101864448*x^24 + 156280253448056209478031589244928*x^22 - 96188116617075838858708654227456*x^20 + 30636368373570166303441645731840*x^18 + 5828527077458909552923002273792*x^16 - 8060049780765551057159394951168*x^14 + 1018074792115156107372011716608*x^12 + 35220131544370794950945931264*x^10 + 327511698517355918956755959808*x^8 - 116978732884218191486738706432*x^6 + 10231563774949176791703149568*x^4 - 366323949299263261553952192*x^2 + 3071435678740442112675625. - Joerg Arndt, Apr 16 2020

			1.94810822885947280327067639...

Violeta Hernández Palacios, Table of n, a(n) for n = 1..20000
Norman W. Johnson, Convex Polyhedra with Regular Faces, Canadian Journal of Mathematics, 18 (1966), 169-200.
H. S. Teoh, The Sphenomegacorona
A. V. Timofeenko, The non-platonic and non-Archimedean noncomposite polyhedra, Journal of Mathematical Sciences, 162(2009), 720-722.
Eric Weisstein's World of Mathematics, Sphenomegacorona.

Volumes of other Johnson solids: A179552, A179587, A179590.

k := Root[-23 - 56 x + 200 x^2 + 304 x^3 - 776 x^4 + 240 x^5 +
   2000 x^6 - 5584 x^7 - 3384 x^8 + 17248 x^9 + 2464 x^10 -
   24576 x^11 + 1568 x^12 + 17216 x^13 - 3712 x^14 - 4800 x^15 +
   1680 x^16, 2];
{{0, 1/2, Sqrt[1 - k^2]}, {k, 1/2, 0}, {0, Sqrt[(3/4 - k^2)/(1 - k^2)] + 1/2, (1/2 - k^2)/Sqrt[1 - k^2]}, {1/2, 0, -Sqrt[1/2 + k - k^2]}, {0, (Sqrt[3/4 - k^2] (2 k^2 - 1))/((k^2 - 1) Sqrt[1 - k^2]) + 1/2, (k^4 - 1/2)/(1 - k^2)^(3/2)}};
v = Union[%, {1, -1, 1}*# & /@ %, {-1, 1, 1}*# & /@ %, {-1, -1,
  1}*# & /@ %];
f := {{2, 3, 12, 11}, {2, 3, 10, 9}, {3, 12, 5}, {3, 10, 5}, {12, 5,
  7}, {10, 5, 7}, {7, 12, 8}, {7, 10, 1}, {12, 8, 11}, {10, 1,
  9}, {8, 1, 7}, {8, 1, 6}, {8, 11, 6}, {1, 9, 6}, {11, 6, 4}, {9,
  6, 4}, {4, 11, 2}, {4, 9, 2}};
RealDigits[N[Volume[Polyhedron[v, f]], 20000]][[1]]

cp's OEIS Frontend

A386852 Decimal expansion of the dihedral angle, in radians, between the pentagonal face and a triangular face in a pentagonal pyramid with equal edges (Johnson solid J_2).

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