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# Polytope of Type {2,10,10}

Atlas Canonical Name : {2,10,10}*400c
if this polytope has a name.
Group : SmallGroup(400,218)
Rank : 4
Schlafli Type : {2,10,10}
Number of vertices, edges, etc : 2, 10, 50, 10
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,10,10,2} of size 800
{2,10,10,4} of size 1600
{2,10,10,5} of size 2000
Vertex Figure Of :
{2,2,10,10} of size 800
{3,2,10,10} of size 1200
{4,2,10,10} of size 1600
{5,2,10,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,5,10}*200
5-fold quotients : {2,10,2}*80
10-fold quotients : {2,5,2}*40
25-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,20,10}*800b, {4,10,10}*800b, {2,10,20}*800c
3-fold covers : {6,10,10}*1200c, {2,10,30}*1200a, {2,30,10}*1200c
4-fold covers : {4,20,10}*1600b, {2,40,10}*1600b, {8,10,10}*1600b, {2,20,20}*1600c, {4,10,20}*1600c, {2,10,40}*1600c
5-fold covers : {2,50,10}*2000b, {2,10,10}*2000a, {10,10,10}*2000e, {10,10,10}*2000f, {2,10,10}*2000d
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (  3, 53)(  4, 57)(  5, 56)(  6, 55)(  7, 54)(  8, 73)(  9, 77)( 10, 76)
( 11, 75)( 12, 74)( 13, 68)( 14, 72)( 15, 71)( 16, 70)( 17, 69)( 18, 63)
( 19, 67)( 20, 66)( 21, 65)( 22, 64)( 23, 58)( 24, 62)( 25, 61)( 26, 60)
( 27, 59)( 28, 78)( 29, 82)( 30, 81)( 31, 80)( 32, 79)( 33, 98)( 34,102)
( 35,101)( 36,100)( 37, 99)( 38, 93)( 39, 97)( 40, 96)( 41, 95)( 42, 94)
( 43, 88)( 44, 92)( 45, 91)( 46, 90)( 47, 89)( 48, 83)( 49, 87)( 50, 86)
( 51, 85)( 52, 84);;
s2 := (  3, 84)(  4, 83)(  5, 87)(  6, 86)(  7, 85)(  8, 79)(  9, 78)( 10, 82)
( 11, 81)( 12, 80)( 13, 99)( 14, 98)( 15,102)( 16,101)( 17,100)( 18, 94)
( 19, 93)( 20, 97)( 21, 96)( 22, 95)( 23, 89)( 24, 88)( 25, 92)( 26, 91)
( 27, 90)( 28, 59)( 29, 58)( 30, 62)( 31, 61)( 32, 60)( 33, 54)( 34, 53)
( 35, 57)( 36, 56)( 37, 55)( 38, 74)( 39, 73)( 40, 77)( 41, 76)( 42, 75)
( 43, 69)( 44, 68)( 45, 72)( 46, 71)( 47, 70)( 48, 64)( 49, 63)( 50, 67)
( 51, 66)( 52, 65);;
s3 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)( 60, 61)
( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)( 80, 81)
( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101);;
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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope