Rectified 120-cell

Four rectifications

120-cell

Rectified 120-cell

600-cell

Rectified 600-cell
Orthogonal projections in H3 Coxeter plane

In geometry, a rectified 120-cell is a uniform 4-polytope formed as the rectification of the regular 120-cell.

E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as tC120.

There are four rectifications of the 120-cell, including the zeroth, the 120-cell itself. The birectified 120-cell is more easily seen as a rectified 600-cell, and the trirectified 120-cell is the same as the dual 600-cell.

Rectified 120-cell

Rectified 120-cell

Schlegel diagram, centered on icosidodecahedon, tetrahedral cells visible
TypeUniform 4-polytope
Uniform index33
Coxeter diagram
Schläfli symbol t1{5,3,3}
or r{5,3,3}
Cells720 total:
120 (3.5.3.5)
600 (3.3.3)
Faces3120 total:
2400 {3}, 720 {5}
Edges3600
Vertices1200
Vertex figure
triangular prism
Symmetry groupH4 or [3,3,5]
Propertiesconvex, vertex-transitive, edge-transitive

In geometry, the rectified 120-cell or rectified hecatonicosachoron is a convex uniform 4-polytope composed of 600 regular tetrahedra and 120 icosidodecahedra cells. Its vertex figure is a triangular prism, with three icosidodecahedra and two tetrahedra meeting at each vertex.

Alternative names:

Projections

3D parallel projection
Parallel projection of the rectified 120-cell into 3D, centered on an icosidodecahedral cell. Nearest cell to 4D viewpoint shown in orange, and tetrahedral cells shown in yellow. Remaining cells culled so that the structure of the projection is visible.
Orthographic projections by Coxeter planes
H4 - F4

[30]

[20]

[12]
H3 A2 / B3 / D4 A3 / B2

[10]

[6]

[4]

Related polytopes

Notes

    References

    External links

    This article is issued from Wikipedia - version of the Thursday, November 19, 2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.