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# Polytope of Type {12,12}

Atlas Canonical Name : {12,12}*384d
if this polytope has a name.
Group : SmallGroup(384,17986)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 16, 96, 16
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{12,12,2} of size 768
{12,12,3} of size 1920
Vertex Figure Of :
{2,12,12} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,6}*192a, {6,12}*192b
4-fold quotients : {3,12}*96, {6,6}*96
8-fold quotients : {3,6}*48, {6,3}*48
16-fold quotients : {3,3}*24
24-fold quotients : {4,2}*16
48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,12}*768a, {24,12}*768b, {12,12}*768a
3-fold covers : {12,12}*1152g, {12,12}*1152p
5-fold covers : {60,12}*1920b, {12,60}*1920d
Permutation Representation (GAP) :
```s0 := (  1, 49)(  2, 50)(  3, 54)(  4, 53)(  5, 52)(  6, 51)(  7, 56)(  8, 55)
(  9, 65)( 10, 66)( 11, 70)( 12, 69)( 13, 68)( 14, 67)( 15, 72)( 16, 71)
( 17, 57)( 18, 58)( 19, 62)( 20, 61)( 21, 60)( 22, 59)( 23, 64)( 24, 63)
( 25, 73)( 26, 74)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 80)( 32, 79)
( 33, 89)( 34, 90)( 35, 94)( 36, 93)( 37, 92)( 38, 91)( 39, 96)( 40, 95)
( 41, 81)( 42, 82)( 43, 86)( 44, 85)( 45, 84)( 46, 83)( 47, 88)( 48, 87)
( 97,145)( 98,146)( 99,150)(100,149)(101,148)(102,147)(103,152)(104,151)
(105,161)(106,162)(107,166)(108,165)(109,164)(110,163)(111,168)(112,167)
(113,153)(114,154)(115,158)(116,157)(117,156)(118,155)(119,160)(120,159)
(121,169)(122,170)(123,174)(124,173)(125,172)(126,171)(127,176)(128,175)
(129,185)(130,186)(131,190)(132,189)(133,188)(134,187)(135,192)(136,191)
(137,177)(138,178)(139,182)(140,181)(141,180)(142,179)(143,184)(144,183);;
s1 := (  1,153)(  2,154)(  3,156)(  4,155)(  5,159)(  6,160)(  7,157)(  8,158)
(  9,145)( 10,146)( 11,148)( 12,147)( 13,151)( 14,152)( 15,149)( 16,150)
( 17,161)( 18,162)( 19,164)( 20,163)( 21,167)( 22,168)( 23,165)( 24,166)
( 25,177)( 26,178)( 27,180)( 28,179)( 29,183)( 30,184)( 31,181)( 32,182)
( 33,169)( 34,170)( 35,172)( 36,171)( 37,175)( 38,176)( 39,173)( 40,174)
( 41,185)( 42,186)( 43,188)( 44,187)( 45,191)( 46,192)( 47,189)( 48,190)
( 49,129)( 50,130)( 51,132)( 52,131)( 53,135)( 54,136)( 55,133)( 56,134)
( 57,121)( 58,122)( 59,124)( 60,123)( 61,127)( 62,128)( 63,125)( 64,126)
( 65,137)( 66,138)( 67,140)( 68,139)( 69,143)( 70,144)( 71,141)( 72,142)
( 73,105)( 74,106)( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)
( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,103)( 86,104)( 87,101)( 88,102)
( 89,113)( 90,114)( 91,116)( 92,115)( 93,119)( 94,120)( 95,117)( 96,118);;
s2 := (  1,  7)(  2,  8)(  5,  6)(  9, 23)( 10, 24)( 11, 19)( 12, 20)( 13, 22)
( 14, 21)( 15, 17)( 16, 18)( 25, 31)( 26, 32)( 29, 30)( 33, 47)( 34, 48)
( 35, 43)( 36, 44)( 37, 46)( 38, 45)( 39, 41)( 40, 42)( 49, 56)( 50, 55)
( 51, 52)( 57, 72)( 58, 71)( 59, 68)( 60, 67)( 61, 69)( 62, 70)( 63, 66)
( 64, 65)( 73, 80)( 74, 79)( 75, 76)( 81, 96)( 82, 95)( 83, 92)( 84, 91)
( 85, 93)( 86, 94)( 87, 90)( 88, 89)( 97,103)( 98,104)(101,102)(105,119)
(106,120)(107,115)(108,116)(109,118)(110,117)(111,113)(112,114)(121,127)
(122,128)(125,126)(129,143)(130,144)(131,139)(132,140)(133,142)(134,141)
(135,137)(136,138)(145,152)(146,151)(147,148)(153,168)(154,167)(155,164)
(156,163)(157,165)(158,166)(159,162)(160,161)(169,176)(170,175)(171,172)
(177,192)(178,191)(179,188)(180,187)(181,189)(182,190)(183,186)(184,185);;
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, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(192)!(  1, 49)(  2, 50)(  3, 54)(  4, 53)(  5, 52)(  6, 51)(  7, 56)
(  8, 55)(  9, 65)( 10, 66)( 11, 70)( 12, 69)( 13, 68)( 14, 67)( 15, 72)
( 16, 71)( 17, 57)( 18, 58)( 19, 62)( 20, 61)( 21, 60)( 22, 59)( 23, 64)
( 24, 63)( 25, 73)( 26, 74)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 80)
( 32, 79)( 33, 89)( 34, 90)( 35, 94)( 36, 93)( 37, 92)( 38, 91)( 39, 96)
( 40, 95)( 41, 81)( 42, 82)( 43, 86)( 44, 85)( 45, 84)( 46, 83)( 47, 88)
( 48, 87)( 97,145)( 98,146)( 99,150)(100,149)(101,148)(102,147)(103,152)
(104,151)(105,161)(106,162)(107,166)(108,165)(109,164)(110,163)(111,168)
(112,167)(113,153)(114,154)(115,158)(116,157)(117,156)(118,155)(119,160)
(120,159)(121,169)(122,170)(123,174)(124,173)(125,172)(126,171)(127,176)
(128,175)(129,185)(130,186)(131,190)(132,189)(133,188)(134,187)(135,192)
(136,191)(137,177)(138,178)(139,182)(140,181)(141,180)(142,179)(143,184)
(144,183);
s1 := Sym(192)!(  1,153)(  2,154)(  3,156)(  4,155)(  5,159)(  6,160)(  7,157)
(  8,158)(  9,145)( 10,146)( 11,148)( 12,147)( 13,151)( 14,152)( 15,149)
( 16,150)( 17,161)( 18,162)( 19,164)( 20,163)( 21,167)( 22,168)( 23,165)
( 24,166)( 25,177)( 26,178)( 27,180)( 28,179)( 29,183)( 30,184)( 31,181)
( 32,182)( 33,169)( 34,170)( 35,172)( 36,171)( 37,175)( 38,176)( 39,173)
( 40,174)( 41,185)( 42,186)( 43,188)( 44,187)( 45,191)( 46,192)( 47,189)
( 48,190)( 49,129)( 50,130)( 51,132)( 52,131)( 53,135)( 54,136)( 55,133)
( 56,134)( 57,121)( 58,122)( 59,124)( 60,123)( 61,127)( 62,128)( 63,125)
( 64,126)( 65,137)( 66,138)( 67,140)( 68,139)( 69,143)( 70,144)( 71,141)
( 72,142)( 73,105)( 74,106)( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)
( 80,110)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,103)( 86,104)( 87,101)
( 88,102)( 89,113)( 90,114)( 91,116)( 92,115)( 93,119)( 94,120)( 95,117)
( 96,118);
s2 := Sym(192)!(  1,  7)(  2,  8)(  5,  6)(  9, 23)( 10, 24)( 11, 19)( 12, 20)
( 13, 22)( 14, 21)( 15, 17)( 16, 18)( 25, 31)( 26, 32)( 29, 30)( 33, 47)
( 34, 48)( 35, 43)( 36, 44)( 37, 46)( 38, 45)( 39, 41)( 40, 42)( 49, 56)
( 50, 55)( 51, 52)( 57, 72)( 58, 71)( 59, 68)( 60, 67)( 61, 69)( 62, 70)
( 63, 66)( 64, 65)( 73, 80)( 74, 79)( 75, 76)( 81, 96)( 82, 95)( 83, 92)
( 84, 91)( 85, 93)( 86, 94)( 87, 90)( 88, 89)( 97,103)( 98,104)(101,102)
(105,119)(106,120)(107,115)(108,116)(109,118)(110,117)(111,113)(112,114)
(121,127)(122,128)(125,126)(129,143)(130,144)(131,139)(132,140)(133,142)
(134,141)(135,137)(136,138)(145,152)(146,151)(147,148)(153,168)(154,167)
(155,164)(156,163)(157,165)(158,166)(159,162)(160,161)(169,176)(170,175)
(171,172)(177,192)(178,191)(179,188)(180,187)(181,189)(182,190)(183,186)
(184,185);
poly := sub<Sym(192)|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, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1 >;

```
References : None.
to this polytope