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# Polytope of Type {12,8}

Atlas Canonical Name : {12,8}*384c
if this polytope has a name.
Group : SmallGroup(384,5573)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 24, 96, 16
Order of s0s1s2 : 3
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{12,8,2} of size 768
Vertex Figure Of :
{2,12,8} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,8}*192a
8-fold quotients : {6,4}*48b
16-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,8}*768k
3-fold covers : {36,8}*1152c, {12,24}*1152h
5-fold covers : {12,40}*1920d, {60,8}*1920c
Permutation Representation (GAP) :
```s0 := (  5,  7)(  6,  8)(  9, 23)( 10, 24)( 11, 21)( 12, 22)( 13, 17)( 14, 18)
( 15, 19)( 16, 20)( 25, 28)( 26, 27)( 29, 30)( 31, 32)( 33, 65)( 34, 66)
( 35, 67)( 36, 68)( 37, 71)( 38, 72)( 39, 69)( 40, 70)( 41, 87)( 42, 88)
( 43, 85)( 44, 86)( 45, 81)( 46, 82)( 47, 83)( 48, 84)( 49, 77)( 50, 78)
( 51, 79)( 52, 80)( 53, 75)( 54, 76)( 55, 73)( 56, 74)( 57, 92)( 58, 91)
( 59, 90)( 60, 89)( 61, 94)( 62, 93)( 63, 96)( 64, 95)( 97, 98)( 99,100)
(101,104)(102,103)(105,120)(106,119)(107,118)(108,117)(109,114)(110,113)
(111,116)(112,115)(121,123)(122,124)(129,162)(130,161)(131,164)(132,163)
(133,168)(134,167)(135,166)(136,165)(137,184)(138,183)(139,182)(140,181)
(141,178)(142,177)(143,180)(144,179)(145,174)(146,173)(147,176)(148,175)
(149,172)(150,171)(151,170)(152,169)(153,187)(154,188)(155,185)(156,186)
(157,189)(158,190)(159,191)(160,192);;
s1 := (  1,129)(  2,130)(  3,134)(  4,133)(  5,132)(  6,131)(  7,135)(  8,136)
(  9,138)( 10,137)( 11,141)( 12,142)( 13,139)( 14,140)( 15,144)( 16,143)
( 17,158)( 18,157)( 19,153)( 20,154)( 21,159)( 22,160)( 23,156)( 24,155)
( 25,147)( 26,148)( 27,152)( 28,151)( 29,146)( 30,145)( 31,149)( 32,150)
( 33, 97)( 34, 98)( 35,102)( 36,101)( 37,100)( 38, 99)( 39,103)( 40,104)
( 41,106)( 42,105)( 43,109)( 44,110)( 45,107)( 46,108)( 47,112)( 48,111)
( 49,126)( 50,125)( 51,121)( 52,122)( 53,127)( 54,128)( 55,124)( 56,123)
( 57,115)( 58,116)( 59,120)( 60,119)( 61,114)( 62,113)( 63,117)( 64,118)
( 65,161)( 66,162)( 67,166)( 68,165)( 69,164)( 70,163)( 71,167)( 72,168)
( 73,170)( 74,169)( 75,173)( 76,174)( 77,171)( 78,172)( 79,176)( 80,175)
( 81,190)( 82,189)( 83,185)( 84,186)( 85,191)( 86,192)( 87,188)( 88,187)
( 89,179)( 90,180)( 91,184)( 92,183)( 93,178)( 94,177)( 95,181)( 96,182);;
s2 := (  1,125)(  2,126)(  3,127)(  4,128)(  5,121)(  6,122)(  7,123)(  8,124)
(  9,117)( 10,118)( 11,119)( 12,120)( 13,113)( 14,114)( 15,115)( 16,116)
( 17,110)( 18,109)( 19,112)( 20,111)( 21,106)( 22,105)( 23,108)( 24,107)
( 25,102)( 26,101)( 27,104)( 28,103)( 29, 98)( 30, 97)( 31,100)( 32, 99)
( 33,157)( 34,158)( 35,159)( 36,160)( 37,153)( 38,154)( 39,155)( 40,156)
( 41,149)( 42,150)( 43,151)( 44,152)( 45,145)( 46,146)( 47,147)( 48,148)
( 49,142)( 50,141)( 51,144)( 52,143)( 53,138)( 54,137)( 55,140)( 56,139)
( 57,134)( 58,133)( 59,136)( 60,135)( 61,130)( 62,129)( 63,132)( 64,131)
( 65,189)( 66,190)( 67,191)( 68,192)( 69,185)( 70,186)( 71,187)( 72,188)
( 73,181)( 74,182)( 75,183)( 76,184)( 77,177)( 78,178)( 79,179)( 80,180)
( 81,174)( 82,173)( 83,176)( 84,175)( 85,170)( 86,169)( 87,172)( 88,171)
( 89,166)( 90,165)( 91,168)( 92,167)( 93,162)( 94,161)( 95,164)( 96,163);;
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*s0*s1*s2*s0*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope