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# Polytope of Type {10,10,2}

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

```

to this polytope