# Noble tetragonal tetracontoctahedron

Noble tetragonal tetracontoctahedron
Rank3
TypeNoble
SpaceSpherical
Elements
Faces48 irregular tetragons
Edges24+24+48
Vertices24
Vertex figureMirror-symmetric octagram
Number of external pieces384
Level of complexity48
Related polytopes
ArmySemi-uniform truncated octahedron
DualNoble faceting of great rhombicuboctahedron
Convex coreNon-Catalan disdyakis dodecahedron
Abstract & topological properties
Flag count384
Euler characteristic–24
OrientableYes
Genus13
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

The noble tetragonal tetracontoctahedron is a noble polyhedron. Its 48 congruent faces are convex irregular quadrilaterals meeting at congruent order-8 vertices. It is a faceting of a semi-uniform truncated octahedral convex hull.

The ratio between the longest and shortest edges is 1:a ≈ 1:1.57021, where a is the positive real root of ${\displaystyle a^6-4a^4+5a^2-3}$.

## Vertex coordinates

The vertex coordinates are all permutations of ${\displaystyle \left(±a,\,±b,\,0\right)}$, where ${\displaystyle \frac{a}{b} = \frac{1+\sqrt[3]{\frac{29-3\sqrt{93}}{2}}+\sqrt[3]{\frac{29+3\sqrt{93}}{2}}}{3} \approx 1.46557}$ is the real root of ${\displaystyle x^3-x^2-1}$.