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

More information Orthogonal projections in H3 Coxeter plane ...

120-cell	Truncated 120-cell	Rectified 120-cell	Bitruncated 120-cell Bitruncated 600-cell
600-cell	Truncated 600-cell	Rectified 600-cell
Orthogonal projections in H3 Coxeter plane

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There are three truncations, including a bitruncation, and a tritruncation, which creates the truncated 600-cell.

Truncated 120-cell
Schlegel diagram (tetrahedron cells visible)
Type	Uniform 4-polytope
Uniform index	36
Schläfli symbol	t0,1{5,3,3} or t{5,3,3}
Coxeter diagrams
Cells	600 3.3.3 120 3.10.10
Faces	2400 triangles 720 decagons
Edges	4800
Vertices	2400
Vertex figure	triangular pyramid
Dual	Tetrakis 600-cell
Symmetry group	H4, [3,3,5], order 14400
Properties	convex

The truncated 120-cell or truncated hecatonicosachoron is a uniform 4-polytope, constructed by a uniform truncation of the regular 120-cell 4-polytope.

It is made of 120 truncated dodecahedral and 600 tetrahedral cells. It has 3120 faces: 2400 being triangles and 720 being decagons. There are 4800 edges of two types: 3600 shared by three truncated dodecahedra and 1200 are shared by two truncated dodecahedra and one tetrahedron. Each vertex has 3 truncated dodecahedra and one tetrahedron around it. Its vertex figure is an equilateral triangular pyramid.

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More information H4, - ...

Orthographic projections by Coxeter planes

H4	-	F4
[30]	[20]	[12]
H3	A2	A3
[10]	[6]	[4]

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Central part of stereographic projection (centered on truncated dodecahedron)

Stereographic projection

More information Bitruncated 120-cell ...

Bitruncated 120-cell
Schlegel diagram, centered on truncated icosahedron, truncated tetrahedral cells visible
Type	Uniform 4-polytope
Uniform index	39
Coxeter diagram
Schläfli symbol	t1,2{5,3,3} or 2t{5,3,3}
Cells	720: 120 5.6.6 600 3.6.6
Faces	4320: 1200{3}+720{5}+ 2400{6}
Edges	7200
Vertices	3600
Vertex figure	digonal disphenoid
Symmetry group	H4, [3,3,5], order 14400
Properties	convex, vertex-transitive

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The bitruncated 120-cell or hexacosihecatonicosachoron is a uniform 4-polytope. It has 720 cells: 120 truncated icosahedra, and 600 truncated tetrahedra. Its vertex figure is a digonal disphenoid, with two truncated icosahedra and two truncated tetrahedra around it.

Truncated 600-cell
Schlegel diagram (icosahedral cells visible)
Type	Uniform 4-polytope
Uniform index	41
Schläfli symbol	t0,1{3,3,5} or t{3,3,5}
Coxeter diagram
Cells	720: 120 3.3.3.3.3 600 3.6.6
Faces	2400{3}+1200{6}
Edges	4320
Vertices	1440
Vertex figure	pentagonal pyramid
Dual	Dodecakis 120-cell
Symmetry group	H4, [3,3,5], order 14400
Properties	convex

The truncated 600-cell or truncated hexacosichoron is a uniform 4-polytope. It is derived from the 600-cell by truncation. It has 720 cells: 120 icosahedra and 600 truncated tetrahedra. Its vertex figure is a pentagonal pyramid, with one icosahedron on the base, and 5 truncated tetrahedra around the sides.