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# Polytope of Type {2,30,12}

Atlas Canonical Name : {2,30,12}*1440c
if this polytope has a name.
Group : SmallGroup(1440,5712)
Rank : 4
Schlafli Type : {2,30,12}
Number of vertices, edges, etc : 2, 30, 180, 12
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,30,6}*720c
3-fold quotients : {2,30,4}*480a
4-fold quotients : {2,15,6}*360
5-fold quotients : {2,6,12}*288c
6-fold quotients : {2,30,2}*240
9-fold quotients : {2,10,4}*160
10-fold quotients : {2,6,6}*144c
12-fold quotients : {2,15,2}*120
15-fold quotients : {2,6,4}*96a
18-fold quotients : {2,10,2}*80
20-fold quotients : {2,3,6}*72
30-fold quotients : {2,6,2}*48
36-fold quotients : {2,5,2}*40
45-fold quotients : {2,2,4}*32
60-fold quotients : {2,3,2}*24
90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 18, 33)
( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 43)( 24, 47)( 25, 46)( 26, 45)
( 27, 44)( 28, 38)( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 49, 52)( 50, 51)
( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 78)( 64, 82)( 65, 81)
( 66, 80)( 67, 79)( 68, 88)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 83)
( 74, 87)( 75, 86)( 76, 85)( 77, 84)( 94, 97)( 95, 96)( 98,103)( 99,107)
(100,106)(101,105)(102,104)(108,123)(109,127)(110,126)(111,125)(112,124)
(113,133)(114,137)(115,136)(116,135)(117,134)(118,128)(119,132)(120,131)
(121,130)(122,129)(139,142)(140,141)(143,148)(144,152)(145,151)(146,150)
(147,149)(153,168)(154,172)(155,171)(156,170)(157,169)(158,178)(159,182)
(160,181)(161,180)(162,179)(163,173)(164,177)(165,176)(166,175)(167,174);;
s2 := (  3,114)(  4,113)(  5,117)(  6,116)(  7,115)(  8,109)(  9,108)( 10,112)
( 11,111)( 12,110)( 13,119)( 14,118)( 15,122)( 16,121)( 17,120)( 18, 99)
( 19, 98)( 20,102)( 21,101)( 22,100)( 23, 94)( 24, 93)( 25, 97)( 26, 96)
( 27, 95)( 28,104)( 29,103)( 30,107)( 31,106)( 32,105)( 33,129)( 34,128)
( 35,132)( 36,131)( 37,130)( 38,124)( 39,123)( 40,127)( 41,126)( 42,125)
( 43,134)( 44,133)( 45,137)( 46,136)( 47,135)( 48,159)( 49,158)( 50,162)
( 51,161)( 52,160)( 53,154)( 54,153)( 55,157)( 56,156)( 57,155)( 58,164)
( 59,163)( 60,167)( 61,166)( 62,165)( 63,144)( 64,143)( 65,147)( 66,146)
( 67,145)( 68,139)( 69,138)( 70,142)( 71,141)( 72,140)( 73,149)( 74,148)
( 75,152)( 76,151)( 77,150)( 78,174)( 79,173)( 80,177)( 81,176)( 82,175)
( 83,169)( 84,168)( 85,172)( 86,171)( 87,170)( 88,179)( 89,178)( 90,182)
( 91,181)( 92,180);;
s3 := ( 18, 33)( 19, 34)( 20, 35)( 21, 36)( 22, 37)( 23, 38)( 24, 39)( 25, 40)
( 26, 41)( 27, 42)( 28, 43)( 29, 44)( 30, 45)( 31, 46)( 32, 47)( 63, 78)
( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)( 70, 85)( 71, 86)
( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 76, 91)( 77, 92)( 93,138)( 94,139)
( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,145)(101,146)(102,147)
(103,148)(104,149)(105,150)(106,151)(107,152)(108,168)(109,169)(110,170)
(111,171)(112,172)(113,173)(114,174)(115,175)(116,176)(117,177)(118,178)
(119,179)(120,180)(121,181)(122,182)(123,153)(124,154)(125,155)(126,156)
(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)
(135,165)(136,166)(137,167);;
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*s3*s2*s1*s2*s1*s2*s1*s2*s1*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*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(182)!(1,2);
s1 := Sym(182)!(  4,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)
( 18, 33)( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 43)( 24, 47)( 25, 46)
( 26, 45)( 27, 44)( 28, 38)( 29, 42)( 30, 41)( 31, 40)( 32, 39)( 49, 52)
( 50, 51)( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 78)( 64, 82)
( 65, 81)( 66, 80)( 67, 79)( 68, 88)( 69, 92)( 70, 91)( 71, 90)( 72, 89)
( 73, 83)( 74, 87)( 75, 86)( 76, 85)( 77, 84)( 94, 97)( 95, 96)( 98,103)
( 99,107)(100,106)(101,105)(102,104)(108,123)(109,127)(110,126)(111,125)
(112,124)(113,133)(114,137)(115,136)(116,135)(117,134)(118,128)(119,132)
(120,131)(121,130)(122,129)(139,142)(140,141)(143,148)(144,152)(145,151)
(146,150)(147,149)(153,168)(154,172)(155,171)(156,170)(157,169)(158,178)
(159,182)(160,181)(161,180)(162,179)(163,173)(164,177)(165,176)(166,175)
(167,174);
s2 := Sym(182)!(  3,114)(  4,113)(  5,117)(  6,116)(  7,115)(  8,109)(  9,108)
( 10,112)( 11,111)( 12,110)( 13,119)( 14,118)( 15,122)( 16,121)( 17,120)
( 18, 99)( 19, 98)( 20,102)( 21,101)( 22,100)( 23, 94)( 24, 93)( 25, 97)
( 26, 96)( 27, 95)( 28,104)( 29,103)( 30,107)( 31,106)( 32,105)( 33,129)
( 34,128)( 35,132)( 36,131)( 37,130)( 38,124)( 39,123)( 40,127)( 41,126)
( 42,125)( 43,134)( 44,133)( 45,137)( 46,136)( 47,135)( 48,159)( 49,158)
( 50,162)( 51,161)( 52,160)( 53,154)( 54,153)( 55,157)( 56,156)( 57,155)
( 58,164)( 59,163)( 60,167)( 61,166)( 62,165)( 63,144)( 64,143)( 65,147)
( 66,146)( 67,145)( 68,139)( 69,138)( 70,142)( 71,141)( 72,140)( 73,149)
( 74,148)( 75,152)( 76,151)( 77,150)( 78,174)( 79,173)( 80,177)( 81,176)
( 82,175)( 83,169)( 84,168)( 85,172)( 86,171)( 87,170)( 88,179)( 89,178)
( 90,182)( 91,181)( 92,180);
s3 := Sym(182)!( 18, 33)( 19, 34)( 20, 35)( 21, 36)( 22, 37)( 23, 38)( 24, 39)
( 25, 40)( 26, 41)( 27, 42)( 28, 43)( 29, 44)( 30, 45)( 31, 46)( 32, 47)
( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)( 69, 84)( 70, 85)
( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 76, 91)( 77, 92)( 93,138)
( 94,139)( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,145)(101,146)
(102,147)(103,148)(104,149)(105,150)(106,151)(107,152)(108,168)(109,169)
(110,170)(111,171)(112,172)(113,173)(114,174)(115,175)(116,176)(117,177)
(118,178)(119,179)(120,180)(121,181)(122,182)(123,153)(124,154)(125,155)
(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)
(134,164)(135,165)(136,166)(137,167);
poly := sub<Sym(182)|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*s3*s2*s1*s2*s1*s2*s1*s2*s1*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*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