List of Truncated Shapes by Schläfli Symbol

The following is a list of truncated shapes by their Schläfli symbols.

## Low Dimensional

In 1 and 0 dimensional polytopes, truncation does not exist.

## 2-Dimensional

### Spherical Tilings

* t

0
,
1

{
1
}

{\displaystyle t\_{0,1} \{1\}}

 - Digon
* t

0
,
1

{
2
}

{\displaystyle t\_{0,1} \{2\}}

 - Square
* t

0
,
1

{
3
}

{\displaystyle t\_{0,1} \{3\}}

 - Hexagon
* t

0
,
1

{
4
}

{\displaystyle t\_{0,1} \{4\}}

 - Octagon
* t

0
,
1

{

4
3

}

{\displaystyle t\_{0,1} \{\frac{4}{3} \}}

 - Octagram
* t

0
,
1

{
5
}

{\displaystyle t\_{0,1} \{5\}}

 - Decagon
* t

0
,
1

{

5
2

}

{\displaystyle t\_{0,1} \{\frac{5}{2} \}}

 - Pentagon
* t

0
,
1

{

5
3

}

{\displaystyle t\_{0,1} \{\frac{5}{3} \}}

 - Decagram
* t

0
,
1

{
6
}

{\displaystyle t\_{0,1} \{6\}}

 - Dodecagon
* t

0
,
1

{

6
5

}

{\displaystyle t\_{0,1} \{\frac{6}{5} \}}

 - Dodecagram
* t

0
,
1

{
7
}

{\displaystyle t\_{0,1} \{ 7 \}}

 - Tetradecagon
* t

0
,
1

{

7
2

}

{\displaystyle t\_{0,1} \{ \frac{7}{2} \}}

 - Heptagon
* t

0
,
1

{

7
3

}

{\displaystyle t\_{0,1} \{\frac{7}{3} \}}

 - Tetradecagram
* t

0
,
1

{

7
5

}

{\displaystyle t\_{0,1} \{ \frac{7}{5} \}}

 - Great Tetradecagram
* t

0
,
1

{
8
}

{\displaystyle t\_{0,1} \{8\}}

 - Hexadecagon
* t

0
,
1

{

8
3

}

{\displaystyle t\_{0,1} \{\frac{8}{3} \}}

 - Small Hexadecagram
* t

0
,
1

{

8
5

}

{\displaystyle t\_{0,1} \{\frac{8}{5} \}}

 - Hexadecagram
* t

0
,
1

{

8
7

}

{\displaystyle t\_{0,1} \{\frac{8}{7} \}}

 - Great Hexadecagram
* t

0
,
1

{
9
}

{\displaystyle t\_{0,1} \{9\}}

 - Octadecagon
* t

0
,
1

{
10
}

{\displaystyle t\_{0,1} \{10\}}

 - Icosagon

## 3-Dimensional

### Spherical Tilings

* t

0
,
1

{
2
,
1
}

{\displaystyle t\_{0,1} \{ 2,1 \}}

 - Monogonal prism
* t

0
,
1

{
2
,
2
}

{\displaystyle t\_{0,1} \{2,2\}}

 - Digonal prism
* t

0
,
1

{
2
,
3
}

{\displaystyle t\_{0,1} \{ 2,3 \}}

 - Triangular prism
* t

0
,
1

{
2
,
4
}

{\displaystyle t\_{0,1} \{2,4\}}

 - Cube
* t

0
,
1

{
2
,
5
}

{\displaystyle t\_{0,1} \{ 2,5 \}}

 - Pentagonal prism
* t

0
,
1

{
2
,
6
}

{\displaystyle t\_{0,1} \{ 2,6 \}}

 - Hexagonal prism
* t

0
,
1

{
2
,
7
}

{\displaystyle t\_{0,1} \{ 2,7 \}}

 - Heptagonal prism
* t

0
,
1

{
2
,
8
}

{\displaystyle t\_{0,1} \{ 2,8 \}}

 - Octagonal prism
* t

0
,
1

{
2
,
9
}

{\displaystyle t\_{0,1} \{ 2,9 \}}

 - Enneagonal prism
* t

0
,
1

{
2
,
10
}

{\displaystyle t\_{0,1} \{ 2,10 \}}

 - Decagonal prism

### Triangular Faces

#### Spherical Tilings

* t

0
,
1

{
3
,
3
}

{\displaystyle t\_{0,1} \{3,3\}}

 - Truncated tetrahedron
* t

0
,
1

{
3
,
4
}

{\displaystyle t\_{0,1} \{3,4\}}

 - Truncated octahedron
* t

0
,
1

{
3
,
5
}

{\displaystyle t\_{0,1} \{3,5\}}

 - Truncated icosahedron

#### Euclidean Tilings

* t

0
,
1

{
3
,
6
}

{\displaystyle t\_{0,1} \{3,6\}}

 - Truncated triangular tiling

### Square Faces

#### Spherical Tilings

* t

0
,
1

{
4
,
3
}

{\displaystyle t\_{0,1} \{4,3\}}

 - Truncated cube

#### Euclidean Tilings

* t

0
,
1

{
4
,
4
}

{\displaystyle t\_{0,1} \{4,4\}}

 - Truncated square tiling

### Pentagonal Faces

#### Spherical Tilings

* t

0
,
1

{
5
,
3
}

{\displaystyle t\_{0,1} \{5,3\}}

 - Truncated dodecagon

### Hexagonal Faces

#### Euclidean Tilings

* t

0
,
1

{
6
,
3
}

{\displaystyle t\_{0,1} \{6,3\}}

 - Truncated hexagonal tiling