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

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

1,2

Comments

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

Links

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.

Example

1.94810822885947280327067639...

Mathematica

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]]

Crossrefs

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

Sequence in context: A113273 A011460 A196522 * A268315 A019659 A155821

Adjacent sequences: A334111 A334112 A334113 * A334115 A334116 A334117

Keyword

nonn,cons

Author

Violeta Hernández Palacios, Apr 14 2020

Status

approved