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# Polytope of Type {2,30,4}

Atlas Canonical Name : {2,30,4}*480b
if this polytope has a name.
Group : SmallGroup(480,1199)
Rank : 4
Schlafli Type : {2,30,4}
Number of vertices, edges, etc : 2, 30, 60, 4
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,30,4,2} of size 960
Vertex Figure Of :
{2,2,30,4} of size 960
{3,2,30,4} of size 1440
{4,2,30,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,15,4}*240
5-fold quotients : {2,6,4}*96c
10-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,60,4}*960b, {2,60,4}*960c, {4,30,4}*960b, {2,30,4}*960
3-fold covers : {2,90,4}*1440b, {6,30,4}*1440d, {6,30,4}*1440e
4-fold covers : {4,60,4}*1920b, {4,60,4}*1920c, {2,30,4}*1920a, {2,120,4}*1920c, {2,120,4}*1920d, {8,30,4}*1920b, {2,60,4}*1920b, {4,30,4}*1920a, {2,30,4}*1920b, {2,60,4}*1920c, {2,30,8}*1920b, {2,30,8}*1920c, {4,30,4}*1920d
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (  4,  5)(  7, 19)(  8, 21)(  9, 20)( 10, 22)( 11, 15)( 12, 17)( 13, 16)
( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)( 29, 60)
( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)( 37, 52)
( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)( 68, 81)
( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)( 84,105)
( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)( 92,117)
( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)(100,109)
(101,108)(102,110);;
s2 := (  3, 87)(  4, 88)(  5, 90)(  6, 89)(  7, 83)(  8, 84)(  9, 86)( 10, 85)
( 11, 99)( 12,100)( 13,102)( 14,101)( 15, 95)( 16, 96)( 17, 98)( 18, 97)
( 19, 91)( 20, 92)( 21, 94)( 22, 93)( 23, 67)( 24, 68)( 25, 70)( 26, 69)
( 27, 63)( 28, 64)( 29, 66)( 30, 65)( 31, 79)( 32, 80)( 33, 82)( 34, 81)
( 35, 75)( 36, 76)( 37, 78)( 38, 77)( 39, 71)( 40, 72)( 41, 74)( 42, 73)
( 43,107)( 44,108)( 45,110)( 46,109)( 47,103)( 48,104)( 49,106)( 50,105)
( 51,119)( 52,120)( 53,122)( 54,121)( 55,115)( 56,116)( 57,118)( 58,117)
( 59,111)( 60,112)( 61,114)( 62,113);;
s3 := (  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)
( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)
( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)
( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)
( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)
( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)
( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)
(115,118)(116,117)(119,122)(120,121);;
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,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*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*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(122)!(1,2);
s1 := Sym(122)!(  4,  5)(  7, 19)(  8, 21)(  9, 20)( 10, 22)( 11, 15)( 12, 17)
( 13, 16)( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)
( 29, 60)( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)
( 37, 52)( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)
( 68, 81)( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)
( 84,105)( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)
( 92,117)( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)
(100,109)(101,108)(102,110);
s2 := Sym(122)!(  3, 87)(  4, 88)(  5, 90)(  6, 89)(  7, 83)(  8, 84)(  9, 86)
( 10, 85)( 11, 99)( 12,100)( 13,102)( 14,101)( 15, 95)( 16, 96)( 17, 98)
( 18, 97)( 19, 91)( 20, 92)( 21, 94)( 22, 93)( 23, 67)( 24, 68)( 25, 70)
( 26, 69)( 27, 63)( 28, 64)( 29, 66)( 30, 65)( 31, 79)( 32, 80)( 33, 82)
( 34, 81)( 35, 75)( 36, 76)( 37, 78)( 38, 77)( 39, 71)( 40, 72)( 41, 74)
( 42, 73)( 43,107)( 44,108)( 45,110)( 46,109)( 47,103)( 48,104)( 49,106)
( 50,105)( 51,119)( 52,120)( 53,122)( 54,121)( 55,115)( 56,116)( 57,118)
( 58,117)( 59,111)( 60,112)( 61,114)( 62,113);
s3 := Sym(122)!(  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)
( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)
( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)
( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)
( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)
( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)
( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)
(112,113)(115,118)(116,117)(119,122)(120,121);
poly := sub<Sym(122)|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, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*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*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