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# Polytope of Type {12,12}

Atlas Canonical Name : {12,12}*384b
if this polytope has a name.
Group : SmallGroup(384,17922)
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
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{12,12,2} of size 768
Vertex Figure Of :
{2,12,12} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,12}*192b, {12,6}*192b
4-fold quotients : {3,12}*96, {12,3}*96, {6,6}*96
8-fold quotients : {3,6}*48, {6,3}*48
16-fold quotients : {3,3}*24
48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,12}*768a
3-fold covers : {12,12}*1152d, {12,12}*1152e
5-fold covers : {12,60}*1920a, {60,12}*1920a
Permutation Representation (GAP) :
```s0 := (  3,  6)(  4,  5)(  7,  8)(  9, 17)( 10, 18)( 11, 22)( 12, 21)( 13, 20)
( 14, 19)( 15, 24)( 16, 23)( 27, 30)( 28, 29)( 31, 32)( 33, 41)( 34, 42)
( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 48)( 40, 47)( 49, 50)( 51, 53)
( 52, 54)( 57, 66)( 58, 65)( 59, 69)( 60, 70)( 61, 67)( 62, 68)( 63, 71)
( 64, 72)( 73, 74)( 75, 77)( 76, 78)( 81, 90)( 82, 89)( 83, 93)( 84, 94)
( 85, 91)( 86, 92)( 87, 95)( 88, 96)( 97,121)( 98,122)( 99,126)(100,125)
(101,124)(102,123)(103,128)(104,127)(105,137)(106,138)(107,142)(108,141)
(109,140)(110,139)(111,144)(112,143)(113,129)(114,130)(115,134)(116,133)
(117,132)(118,131)(119,136)(120,135)(145,170)(146,169)(147,173)(148,174)
(149,171)(150,172)(151,175)(152,176)(153,186)(154,185)(155,189)(156,190)
(157,187)(158,188)(159,191)(160,192)(161,178)(162,177)(163,181)(164,182)
(165,179)(166,180)(167,183)(168,184);;
s1 := (  1,105)(  2,106)(  3,108)(  4,107)(  5,111)(  6,112)(  7,109)(  8,110)
(  9, 97)( 10, 98)( 11,100)( 12, 99)( 13,103)( 14,104)( 15,101)( 16,102)
( 17,113)( 18,114)( 19,116)( 20,115)( 21,119)( 22,120)( 23,117)( 24,118)
( 25,129)( 26,130)( 27,132)( 28,131)( 29,135)( 30,136)( 31,133)( 32,134)
( 33,121)( 34,122)( 35,124)( 36,123)( 37,127)( 38,128)( 39,125)( 40,126)
( 41,137)( 42,138)( 43,140)( 44,139)( 45,143)( 46,144)( 47,141)( 48,142)
( 49,154)( 50,153)( 51,155)( 52,156)( 53,160)( 54,159)( 55,158)( 56,157)
( 57,146)( 58,145)( 59,147)( 60,148)( 61,152)( 62,151)( 63,150)( 64,149)
( 65,162)( 66,161)( 67,163)( 68,164)( 69,168)( 70,167)( 71,166)( 72,165)
( 73,178)( 74,177)( 75,179)( 76,180)( 77,184)( 78,183)( 79,182)( 80,181)
( 81,170)( 82,169)( 83,171)( 84,172)( 85,176)( 86,175)( 87,174)( 88,173)
( 89,186)( 90,185)( 91,187)( 92,188)( 93,192)( 94,191)( 95,190)( 96,189);;
s2 := (  1, 55)(  2, 56)(  3, 51)(  4, 52)(  5, 54)(  6, 53)(  7, 49)(  8, 50)
(  9, 71)( 10, 72)( 11, 67)( 12, 68)( 13, 70)( 14, 69)( 15, 65)( 16, 66)
( 17, 63)( 18, 64)( 19, 59)( 20, 60)( 21, 62)( 22, 61)( 23, 57)( 24, 58)
( 25, 79)( 26, 80)( 27, 75)( 28, 76)( 29, 78)( 30, 77)( 31, 73)( 32, 74)
( 33, 95)( 34, 96)( 35, 91)( 36, 92)( 37, 94)( 38, 93)( 39, 89)( 40, 90)
( 41, 87)( 42, 88)( 43, 83)( 44, 84)( 45, 86)( 46, 85)( 47, 81)( 48, 82)
( 97,175)( 98,176)( 99,171)(100,172)(101,174)(102,173)(103,169)(104,170)
(105,191)(106,192)(107,187)(108,188)(109,190)(110,189)(111,185)(112,186)
(113,183)(114,184)(115,179)(116,180)(117,182)(118,181)(119,177)(120,178)
(121,151)(122,152)(123,147)(124,148)(125,150)(126,149)(127,145)(128,146)
(129,167)(130,168)(131,163)(132,164)(133,166)(134,165)(135,161)(136,162)
(137,159)(138,160)(139,155)(140,156)(141,158)(142,157)(143,153)(144,154);;
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*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*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*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope