# Polytope of Type {2,20,10}

Atlas Canonical Name : {2,20,10}*800a
if this polytope has a name.
Group : SmallGroup(800,1127)
Rank : 4
Schlafli Type : {2,20,10}
Number of vertices, edges, etc : 2, 20, 100, 10
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,20,10,2} of size 1600
Vertex Figure Of :
{2,2,20,10} of size 1600
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,10,10}*400a
5-fold quotients : {2,20,2}*160, {2,4,10}*160
10-fold quotients : {2,2,10}*80, {2,10,2}*80
20-fold quotients : {2,2,5}*40, {2,5,2}*40
25-fold quotients : {2,4,2}*32
50-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,20,10}*1600a, {2,40,10}*1600a, {2,20,20}*1600a
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (  8, 23)(  9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 18)( 14, 19)( 15, 20)
( 16, 21)( 17, 22)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 43)
( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 53, 78)( 54, 79)( 55, 80)( 56, 81)
( 57, 82)( 58, 98)( 59, 99)( 60,100)( 61,101)( 62,102)( 63, 93)( 64, 94)
( 65, 95)( 66, 96)( 67, 97)( 68, 88)( 69, 89)( 70, 90)( 71, 91)( 72, 92)
( 73, 83)( 74, 84)( 75, 85)( 76, 86)( 77, 87);;
s2 := (  3, 58)(  4, 62)(  5, 61)(  6, 60)(  7, 59)(  8, 53)(  9, 57)( 10, 56)
( 11, 55)( 12, 54)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)( 18, 68)
( 19, 72)( 20, 71)( 21, 70)( 22, 69)( 23, 63)( 24, 67)( 25, 66)( 26, 65)
( 27, 64)( 28, 83)( 29, 87)( 30, 86)( 31, 85)( 32, 84)( 33, 78)( 34, 82)
( 35, 81)( 36, 80)( 37, 79)( 38, 98)( 39,102)( 40,101)( 41,100)( 42, 99)
( 43, 93)( 44, 97)( 45, 96)( 46, 95)( 47, 94)( 48, 88)( 49, 92)( 50, 91)
( 51, 90)( 52, 89);;
s3 := (  3,  4)(  5,  7)(  8,  9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)( 20, 22)
( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)( 40, 42)
( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)( 60, 62)
( 63, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)( 75, 77)( 78, 79)( 80, 82)
( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93, 94)( 95, 97)( 98, 99)(100,102);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(102)!(1,2);
s1 := Sym(102)!(  8, 23)(  9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 18)( 14, 19)
( 15, 20)( 16, 21)( 17, 22)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)
( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 53, 78)( 54, 79)( 55, 80)
( 56, 81)( 57, 82)( 58, 98)( 59, 99)( 60,100)( 61,101)( 62,102)( 63, 93)
( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68, 88)( 69, 89)( 70, 90)( 71, 91)
( 72, 92)( 73, 83)( 74, 84)( 75, 85)( 76, 86)( 77, 87);
s2 := Sym(102)!(  3, 58)(  4, 62)(  5, 61)(  6, 60)(  7, 59)(  8, 53)(  9, 57)
( 10, 56)( 11, 55)( 12, 54)( 13, 73)( 14, 77)( 15, 76)( 16, 75)( 17, 74)
( 18, 68)( 19, 72)( 20, 71)( 21, 70)( 22, 69)( 23, 63)( 24, 67)( 25, 66)
( 26, 65)( 27, 64)( 28, 83)( 29, 87)( 30, 86)( 31, 85)( 32, 84)( 33, 78)
( 34, 82)( 35, 81)( 36, 80)( 37, 79)( 38, 98)( 39,102)( 40,101)( 41,100)
( 42, 99)( 43, 93)( 44, 97)( 45, 96)( 46, 95)( 47, 94)( 48, 88)( 49, 92)
( 50, 91)( 51, 90)( 52, 89);
s3 := Sym(102)!(  3,  4)(  5,  7)(  8,  9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)
( 20, 22)( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)
( 40, 42)( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)
( 60, 62)( 63, 64)( 65, 67)( 68, 69)( 70, 72)( 73, 74)( 75, 77)( 78, 79)
( 80, 82)( 83, 84)( 85, 87)( 88, 89)( 90, 92)( 93, 94)( 95, 97)( 98, 99)
(100,102);
poly := sub<Sym(102)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope