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# Polytope of Type {10,10}

Atlas Canonical Name : {10,10}*200c
if this polytope has a name.
Group : SmallGroup(200,49)
Rank : 3
Schlafli Type : {10,10}
Number of vertices, edges, etc : 10, 50, 10
Order of s0s1s2 : 10
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{10,10,2} of size 400
{10,10,4} of size 800
{10,10,5} of size 1000
{10,10,6} of size 1200
{10,10,8} of size 1600
{10,10,10} of size 2000
{10,10,10} of size 2000
Vertex Figure Of :
{2,10,10} of size 400
{4,10,10} of size 800
{6,10,10} of size 1200
{8,10,10} of size 1600
{10,10,10} of size 2000
{10,10,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,10}*100
5-fold quotients : {10,2}*40
10-fold quotients : {5,2}*20
25-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,10}*400b, {10,20}*400c
3-fold covers : {10,30}*600a, {30,10}*600c
4-fold covers : {40,10}*800b, {20,20}*800c, {10,40}*800c
5-fold covers : {50,10}*1000b, {10,10}*1000a, {10,10}*1000d
6-fold covers : {20,30}*1200a, {10,60}*1200a, {60,10}*1200c, {30,20}*1200c
7-fold covers : {10,70}*1400a, {70,10}*1400c
8-fold covers : {80,10}*1600b, {20,40}*1600a, {20,20}*1600c, {20,40}*1600b, {40,20}*1600d, {40,20}*1600f, {10,80}*1600c
9-fold covers : {10,90}*1800a, {90,10}*1800c, {30,30}*1800e, {30,30}*1800f, {30,30}*1800i
10-fold covers : {100,10}*2000b, {20,10}*2000a, {50,20}*2000b, {10,20}*2000c, {10,20}*2000h, {20,10}*2000h
Permutation Representation (GAP) :
```s0 := (  1, 51)(  2, 55)(  3, 54)(  4, 53)(  5, 52)(  6, 71)(  7, 75)(  8, 74)
(  9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)( 16, 61)
( 17, 65)( 18, 64)( 19, 63)( 20, 62)( 21, 56)( 22, 60)( 23, 59)( 24, 58)
( 25, 57)( 26, 76)( 27, 80)( 28, 79)( 29, 78)( 30, 77)( 31, 96)( 32,100)
( 33, 99)( 34, 98)( 35, 97)( 36, 91)( 37, 95)( 38, 94)( 39, 93)( 40, 92)
( 41, 86)( 42, 90)( 43, 89)( 44, 88)( 45, 87)( 46, 81)( 47, 85)( 48, 84)
( 49, 83)( 50, 82);;
s1 := (  1, 82)(  2, 81)(  3, 85)(  4, 84)(  5, 83)(  6, 77)(  7, 76)(  8, 80)
(  9, 79)( 10, 78)( 11, 97)( 12, 96)( 13,100)( 14, 99)( 15, 98)( 16, 92)
( 17, 91)( 18, 95)( 19, 94)( 20, 93)( 21, 87)( 22, 86)( 23, 90)( 24, 89)
( 25, 88)( 26, 57)( 27, 56)( 28, 60)( 29, 59)( 30, 58)( 31, 52)( 32, 51)
( 33, 55)( 34, 54)( 35, 53)( 36, 72)( 37, 71)( 38, 75)( 39, 74)( 40, 73)
( 41, 67)( 42, 66)( 43, 70)( 44, 69)( 45, 68)( 46, 62)( 47, 61)( 48, 65)
( 49, 64)( 50, 63);;
s2 := (  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);;
poly := Group([s0,s1,s2]);;

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

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

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

```
References : None.
to this polytope