Second noble octagrammic triacontahedron

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Second noble octagrammic triacontahedron
Rank3
TypeNoble
Elements
Faces30 rectangular-symmetric octagrams
Edges60+60
Vertices60
Vertex figureButterfly
Measures (edge lengths , )
Edge length ratio
Circumradius
Related polytopes
ArmySrid
DualThird noble faceting of icosidodecahedron
ConjugateNoble octagonal triacontahedron
Convex coreRhombic triacontahedron
Abstract & topological properties
Flag count480
Euler characteristic–30
OrientableNo
Genus32
Properties
SymmetryH3, order 120
Flag orbits4
ConvexNo
NatureTame
History
Discovered byMax Brückner
First discovered1906


The second noble octagrammic triacontahedron is a noble polyhedron. Its 30 congruent faces are rectangular-symmetric octagrams meeting at congruent order-4 vertices. It is a faceting of a uniform small rhombicosidodecahedron hull.

The ratio between the shortest and longest edges is 1: ≈ 1:1.37638.

Vertex coordinates[edit | edit source]

A second noble octagrammic triacontahedron, centered at the origin, has vertex coordinates given by all permutations of

  • ,

along with all even permutations of

  • ,
  • .

Other noble polyhedra that can have these coordinates are the Crennell number 4 stellation of the icosahedron and the third noble unihexagrammic hexecontahedron.