![]() 120-cell ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Rectified 120-cell ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ||
![]() 600-cell ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Rectified 600-cell ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ||
Orthogonal projections in H3 Coxeter plane |
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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 | |
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![]() Schlegel diagram, centered on icosidodecahedon, tetrahedral cells visible | |
Type | Uniform 4-polytope |
Uniform index | 33 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Schläfli symbol | t1{5,3,3} or r{5,3,3} |
Cells | 720 total: 120 (3.5.3.5) ![]() 600 (3.3.3) ![]() |
Faces | 3120 total: 2400 {3}, 720 {5} |
Edges | 3600 |
Vertices | 1200 |
Vertex figure |
![]() triangular prism |
Symmetry group | H4 or [3,3,5] |
Properties | convex, 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:
H4 | - | F4 |
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![]() [30] |
![]() [20] |
![]() [12] |
H3 | A2 / B3 / D4 | A3 / B2 |
![]() [10] |
![]() [6] |
![]() [4] |
H4 family polytopes | |||||||||||
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120-cell |
rectified 120-cell |
truncated 120-cell |
cantellated 120-cell |
runcinated 120-cell |
cantitruncated 120-cell |
runcitruncated 120-cell |
omnitruncated 120-cell | ||||
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{5,3,3} | r{5,3,3} | t{5,3,3} | rr{5,3,3} | t0,3{5,3,3} | tr{5,3,3} | t0,1,3{5,3,3} | t0,1,2,3{5,3,3} | ||||
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600-cell |
rectified 600-cell |
truncated 600-cell |
cantellated 600-cell |
bitruncated 600-cell |
cantitruncated 600-cell |
runcitruncated 600-cell |
omnitruncated 600-cell | ||||
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{3,3,5} | r{3,3,5} | t{3,3,5} | rr{3,3,5} | 2t{3,3,5} | tr{3,3,5} | t0,1,3{3,3,5} | t0,1,2,3{3,3,5} |