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Truncated 120-cells

Uniform 4-polytope From Wikipedia, the free encyclopedia

Truncated 120-cells
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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 ...

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

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Truncated 120-cell

Summarize
Perspective
Truncated 120-cell
Thumb
Schlegel diagram
(tetrahedron cells visible)
TypeUniform 4-polytope
Uniform index36
Schläfli symbolt0,1{5,3,3}
or t{5,3,3}
Coxeter diagrams
Cells600 3.3.3
120 3.10.10
Faces2400 triangles
720 decagons
Edges4800
Vertices2400
Vertex figureThumb
triangular pyramid
DualTetrakis 600-cell
Symmetry groupH4, [3,3,5], order 14400
Propertiesconvex
Thumb
Net

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.

Alternate names

  • Truncated 120-cell (Norman W. Johnson)
    • Tuncated hecatonicosachoron / Truncated dodecacontachoron / Truncated polydodecahedron
  • Truncated-icosahedral hexacosihecatonicosachoron (Acronym thi) (George Olshevsky, and Jonathan Bowers)[1]

Images

More information H4, - ...
Thumb
net
Thumb
Central part of stereographic projection
(centered on truncated dodecahedron)
Thumb
Stereographic projection
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Bitruncated 120-cell

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More information Bitruncated 120-cell ...
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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.

Alternate names

  • Bitruncated 120-cell / Bitruncated 600-cell (Norman W. Johnson)
    • Bitruncated hecatonicosachoron / Bitruncated hexacosichoron / Bitruncated polydodecahedron / Bitruncated polytetrahedron
  • Truncated-icosahedral hexacosihecatonicosachoron (Acronym Xhi) (George Olshevsky, and Jonathan Bowers)[2]

Images

Thumb
Stereographic projection (Close up)
More information H3, A2 / B3 / D4 ...
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Truncated 600-cell

Summarize
Perspective
Truncated 600-cell
Thumb
Schlegel diagram
(icosahedral cells visible)
TypeUniform 4-polytope
Uniform index41
Schläfli symbolt0,1{3,3,5}
or t{3,3,5}
Coxeter diagram
Cells720:
120 3.3.3.3.3
600 3.6.6
Faces2400{3}+1200{6}
Edges4320
Vertices1440
Vertex figureThumb
pentagonal pyramid
DualDodecakis 120-cell
Symmetry groupH4, [3,3,5], order 14400
Propertiesconvex
Thumb
Net

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.

Alternate names

  • Truncated 600-cell (Norman W. Johnson)
  • Truncated hexacosichoron (Acronym tex) (George Olshevsky, and Jonathan Bowers)[3]
  • Truncated tetraplex (Conway)

Structure

The truncated 600-cell consists of 600 truncated tetrahedra and 120 icosahedra. The truncated tetrahedral cells are joined to each other via their hexagonal faces, and to the icosahedral cells via their triangular faces. Each icosahedron is surrounded by 20 truncated tetrahedra.

Images

Stereographic projection or Schlegel diagrams
Thumb
Centered on icosahedron
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Centered on truncated tetrahedron
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Central part
and some of 120 red icosahedra.
Thumb
Net
More information H4, - ...
More information 3D Parallel projection ...
More information H4 family polytopes, 120-cell ...
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Notes

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References

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