Second noble triangular hecatonicosahedron

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Second noble triangular hecatonicosahedron
Rank3
TypeNoble
Elements
Faces120 scalene triangles
Edges60+60+60
Vertices30
Vertex figureRectangular-symmetric dodecagram
Measures (edge lengths , , )
Circumradius
Number of external pieces720
Level of complexity40
Related polytopes
ArmyId
DualFifth noble stellation of rhombic triacontahedron
ConjugateFirst noble triangular hecatonicosahedron
Convex coreDisdyakis triacontahedron
Abstract & topological properties
Flag count720
Euler characteristic–30
OrientableYes
Genus16
Properties
SymmetryH3, order 120
Flag orbits6
ConvexNo
NatureTame
History
Discovered byEdmond Hess
First discovered1876


The second noble triangular hecatonicosahedron is a noble polyhedron. Its 120 congruent faces are scalene triangles meeting at congruent order-12 vertices. It is a faceting of a uniform icosidodecahedron hull.

The ratio between the shortest and longest edges is 1: ≈ 1:1.47337.

The triangular faces are similar to the vertex figure of the great quasitruncated icosidodecahedron.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of an icosidodecahedron.