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BITRUNCATION

Bitruncation

Operation in Euclidean geometry

In geometry, a bitruncation is an operation on regular polytopes. The original edges are lost completely and the original faces remain as smaller copies

Bitruncation

Truncation (geometry)

Operation that cuts polytope vertices, creating a new facet in place of each vertex

truncated cube; it is represented by a Schläfli symbol t{p,q,...}. A bitruncation is a deeper truncation, removing all the original edges, but leaving

Truncation (geometry)

Truncation_(geometry)

Truncated tesseract

Type of tesseract

truncation of the regular tesseract. There are three truncations, including a bitruncation, and a tritruncation, which creates the truncated 16-cell. The truncated

Truncated tesseract

Truncated_tesseract

Truncated 120-cells

Uniform 4-polytope

truncation of the regular 120-cell. There are three truncations, including a bitruncation, and a tritruncation, which creates the truncated 600-cell. The truncated

Truncated 120-cells

Truncated_120-cells

Truncated 5-cell

the regular 5-cell. There are two degrees of truncations, including a bitruncation. The truncated 5-cell, truncated pentachoron or truncated 4-simplex is

Truncated 5-cell

Truncated_5-cell

Schläfli symbol

Notation for polytopes and tessellations

a 4-polytope's symbol is palindromic (e.g. {3,3,3} or {3,4,3}), its bitruncation will only have truncated forms of the vertex figure as cells. For higher-dimensional

Schläfli symbol

Schläfli_symbol

Truncated 24-cells

the regular 24-cell. There are two degrees of truncations, including a bitruncation. The truncated 24-cell or truncated icositetrachoron is a uniform 4-dimensional

Truncated 24-cells

Truncated_24-cells

Conway polyhedron notation

Method of describing higher-order polyhedra

vertices but leaves a portion of the original edges. Zip is also called bitruncation. 4 [ 1 1 1 0 4 0 0 2 0 ] {\displaystyle {\begin{bmatrix}1&1&1\\0&4&0

Conway polyhedron notation

Conway_polyhedron_notation

Truncated 5-simplexes

5-simplex are located as pairs on the edge of the 5-simplex. Vertices of the bitruncation 5-simplex are located on the triangular faces of the 5-simplex. The truncated

Truncated 5-simplexes

Truncated_5-simplexes

Uniform polyhedron

Isogonal polyhedron with regular faces

the dual. Bitruncated (2t) (also truncated dual) 2t{p,q} t1,2{p,q} A bitruncation can be seen as the truncation of the dual. A bitruncated cube is a truncated

Uniform polyhedron

Uniform_polyhedron

Versor

Quaternion of norm 1 (unit quaternion)

group elements, taken as points on S3, form a 24-cell. By a process of bitruncation of the 24-cell, the 48-cell on G is obtained, and these versors multiply

Versor

Uniform 4-polytope

Class of 4-dimensional polytopes

naming scheme for the indexed ring permutations beyond truncation and bitruncation, and all of Johnson's names were included in the book index. Nonregular

Uniform 4-polytope

Uniform_4-polytope

Rectification (geometry)

Operation in Euclidean geometry

the same as a rectified {r,q,p}, however. A further truncation, called bitruncation, is symmetric between a 4-polytope and its dual. See Uniform 4-polytope#Geometric

Rectification (geometry)

Rectification_(geometry)

Bitruncated tesseractic honeycomb

tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a bitruncation of a tesseractic honeycomb. It is also called a cantic quarter tesseractic

Bitruncated tesseractic honeycomb

Bitruncated_tesseractic_honeycomb

Alternation (geometry)

Removal of alternate vertices

Polyhedron operators v t e Seed Truncation Rectification Bitruncation Dual Expansion Omnitruncation Alternations t0{p,q} {p,q} t01{p,q} t{p,q} t1{p,q}

Alternation (geometry)

Alternation_(geometry)

Uniform polytope

Isogonal polytope with uniform facets

from Latin truncare 'to cut off'.) There are higher truncations also: bitruncation t1,2 or 2t, tritruncation t2,3 or 3t, quadritruncation t3,4 or 4t, quintitruncation

Uniform polytope

Uniform_polytope

Truncated 5-orthoplexes

permutations of (±2,±2,±1,0,0) The bitruncated 5-orthoplex is constructed by a bitruncation operation applied to the 5-orthoplex. The truncated 5-orthoplex and bitruncated

Truncated 5-orthoplexes

Truncated_5-orthoplexes

List of polygons, polyhedra and polytopes

hypercubic honeycomb Rectification (geometry) Truncation (geometry) Bitruncation Cantellation Runcination Sterication Omnitruncation Expansion (geometry)

List of polygons, polyhedra and polytopes

List_of_polygons,_polyhedra_and_polytopes

Omnitruncation

Geometric operation

Polyhedron operators v t e Seed Truncation Rectification Bitruncation Dual Expansion Omnitruncation Alternations t0{p,q} {p,q} t01{p,q} t{p,q} t1{p,q}

Omnitruncation

Expansion (geometry)

Geometric operation on convex polytopes

Polyhedron operators v t e Seed Truncation Rectification Bitruncation Dual Expansion Omnitruncation Alternations t0{p,q} {p,q} t01{p,q} t{p,q} t1{p,q}

Expansion (geometry)

Expansion_(geometry)

Omnitruncated polyhedron

Polyhedron operators v t e Seed Truncation Rectification Bitruncation Dual Expansion Omnitruncation Alternations t0{p,q} {p,q} t01{p,q} t{p,q} t1{p,q}

Omnitruncated polyhedron

Omnitruncated_polyhedron

Snub polyhedron

Polyhedron resulting from the snub operation

Polyhedron operators v t e Seed Truncation Rectification Bitruncation Dual Expansion Omnitruncation Alternations t0{p,q} {p,q} t01{p,q} t{p,q} t1{p,q}

Snub polyhedron

Snub_polyhedron

Snub (geometry)

Geometric operation applied to a polyhedron

Polyhedron operators v t e Seed Truncation Rectification Bitruncation Dual Expansion Omnitruncation Alternations t0{p,q} {p,q} t01{p,q} t{p,q} t1{p,q}

Snub (geometry)

Snub_(geometry)

Uniform tilings in hyperbolic plane

Symmetric subdivision in hyperbolic geometry

icosidodecahedron Trihexagonal tiling Triheptagonal tiling Trioctagonal tiling Bitruncation (2t) Dual kis (dk) 2t{p,q} truncated triangular dihedron (Half of the

Uniform tilings in hyperbolic plane

Uniform_tilings_in_hyperbolic_plane