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# Polytope of Type {2,10,10}

Atlas Canonical Name : {2,10,10}*400a
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) :
5-fold quotients : {2,2,10}*80, {2,10,2}*80
10-fold quotients : {2,2,5}*40, {2,5,2}*40
25-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,10,20}*800a, {2,20,10}*800a, {4,10,10}*800a
3-fold covers : {6,10,10}*1200a, {2,10,30}*1200b, {2,30,10}*1200b
4-fold covers : {4,10,20}*1600a, {4,20,10}*1600a, {2,10,40}*1600a, {2,40,10}*1600a, {8,10,10}*1600a, {2,20,20}*1600a
5-fold covers : {2,10,50}*2000a, {2,50,10}*2000a, {2,10,10}*2000c, {10,10,10}*2000b, {10,10,10}*2000d, {2,10,10}*2000d
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (  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);;
s2 := (  3, 54)(  4, 53)(  5, 57)(  6, 56)(  7, 55)(  8, 74)(  9, 73)( 10, 77)
( 11, 76)( 12, 75)( 13, 69)( 14, 68)( 15, 72)( 16, 71)( 17, 70)( 18, 64)
( 19, 63)( 20, 67)( 21, 66)( 22, 65)( 23, 59)( 24, 58)( 25, 62)( 26, 61)
( 27, 60)( 28, 79)( 29, 78)( 30, 82)( 31, 81)( 32, 80)( 33, 99)( 34, 98)
( 35,102)( 36,101)( 37,100)( 38, 94)( 39, 93)( 40, 97)( 41, 96)( 42, 95)
( 43, 89)( 44, 88)( 45, 92)( 46, 91)( 47, 90)( 48, 84)( 49, 83)( 50, 87)
( 51, 86)( 52, 85);;
s3 := (  3, 83)(  4, 84)(  5, 85)(  6, 86)(  7, 87)(  8, 78)(  9, 79)( 10, 80)
( 11, 81)( 12, 82)( 13, 98)( 14, 99)( 15,100)( 16,101)( 17,102)( 18, 93)
( 19, 94)( 20, 95)( 21, 96)( 22, 97)( 23, 88)( 24, 89)( 25, 90)( 26, 91)
( 27, 92)( 28, 58)( 29, 59)( 30, 60)( 31, 61)( 32, 62)( 33, 53)( 34, 54)
( 35, 55)( 36, 56)( 37, 57)( 38, 73)( 39, 74)( 40, 75)( 41, 76)( 42, 77)
( 43, 68)( 44, 69)( 45, 70)( 46, 71)( 47, 72)( 48, 63)( 49, 64)( 50, 65)
( 51, 66)( 52, 67);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

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

```

to this polytope