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# Polytope of Type {2,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4}*768c
if this polytope has a name.
Group : SmallGroup(768,1087527)
Rank : 4
Schlafli Type : {2,12,4}
Number of vertices, edges, etc : 2, 48, 96, 16
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {2,6,4}*384a
4-fold quotients : {2,12,4}*192c
8-fold quotients : {2,6,4}*96c
16-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  5,  6)(  7, 11)(  8, 12)(  9, 14)( 10, 13)( 17, 18)( 19, 35)( 20, 36)
( 21, 38)( 22, 37)( 23, 43)( 24, 44)( 25, 46)( 26, 45)( 27, 39)( 28, 40)
( 29, 42)( 30, 41)( 31, 47)( 32, 48)( 33, 50)( 34, 49)( 53, 54)( 55, 59)
( 56, 60)( 57, 62)( 58, 61)( 65, 66)( 67, 83)( 68, 84)( 69, 86)( 70, 85)
( 71, 91)( 72, 92)( 73, 94)( 74, 93)( 75, 87)( 76, 88)( 77, 90)( 78, 89)
( 79, 95)( 80, 96)( 81, 98)( 82, 97)( 99,147)(100,148)(101,150)(102,149)
(103,155)(104,156)(105,158)(106,157)(107,151)(108,152)(109,154)(110,153)
(111,159)(112,160)(113,162)(114,161)(115,179)(116,180)(117,182)(118,181)
(119,187)(120,188)(121,190)(122,189)(123,183)(124,184)(125,186)(126,185)
(127,191)(128,192)(129,194)(130,193)(131,163)(132,164)(133,166)(134,165)
(135,171)(136,172)(137,174)(138,173)(139,167)(140,168)(141,170)(142,169)
(143,175)(144,176)(145,178)(146,177);;
s2 := (  3,115)(  4,118)(  5,117)(  6,116)(  7,121)(  8,120)(  9,119)( 10,122)
( 11,128)( 12,129)( 13,130)( 14,127)( 15,126)( 16,123)( 17,124)( 18,125)
( 19, 99)( 20,102)( 21,101)( 22,100)( 23,105)( 24,104)( 25,103)( 26,106)
( 27,112)( 28,113)( 29,114)( 30,111)( 31,110)( 32,107)( 33,108)( 34,109)
( 35,131)( 36,134)( 37,133)( 38,132)( 39,137)( 40,136)( 41,135)( 42,138)
( 43,144)( 44,145)( 45,146)( 46,143)( 47,142)( 48,139)( 49,140)( 50,141)
( 51,163)( 52,166)( 53,165)( 54,164)( 55,169)( 56,168)( 57,167)( 58,170)
( 59,176)( 60,177)( 61,178)( 62,175)( 63,174)( 64,171)( 65,172)( 66,173)
( 67,147)( 68,150)( 69,149)( 70,148)( 71,153)( 72,152)( 73,151)( 74,154)
( 75,160)( 76,161)( 77,162)( 78,159)( 79,158)( 80,155)( 81,156)( 82,157)
( 83,179)( 84,182)( 85,181)( 86,180)( 87,185)( 88,184)( 89,183)( 90,186)
( 91,192)( 92,193)( 93,194)( 94,191)( 95,190)( 96,187)( 97,188)( 98,189);;
s3 := (  3, 63)(  4, 64)(  5, 65)(  6, 66)(  7, 59)(  8, 60)(  9, 61)( 10, 62)
( 11, 55)( 12, 56)( 13, 57)( 14, 58)( 15, 51)( 16, 52)( 17, 53)( 18, 54)
( 19, 79)( 20, 80)( 21, 81)( 22, 82)( 23, 75)( 24, 76)( 25, 77)( 26, 78)
( 27, 71)( 28, 72)( 29, 73)( 30, 74)( 31, 67)( 32, 68)( 33, 69)( 34, 70)
( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 91)( 40, 92)( 41, 93)( 42, 94)
( 43, 87)( 44, 88)( 45, 89)( 46, 90)( 47, 83)( 48, 84)( 49, 85)( 50, 86)
( 99,159)(100,160)(101,161)(102,162)(103,155)(104,156)(105,157)(106,158)
(107,151)(108,152)(109,153)(110,154)(111,147)(112,148)(113,149)(114,150)
(115,175)(116,176)(117,177)(118,178)(119,171)(120,172)(121,173)(122,174)
(123,167)(124,168)(125,169)(126,170)(127,163)(128,164)(129,165)(130,166)
(131,191)(132,192)(133,193)(134,194)(135,187)(136,188)(137,189)(138,190)
(139,183)(140,184)(141,185)(142,186)(143,179)(144,180)(145,181)(146,182);;
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, s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!(  5,  6)(  7, 11)(  8, 12)(  9, 14)( 10, 13)( 17, 18)( 19, 35)
( 20, 36)( 21, 38)( 22, 37)( 23, 43)( 24, 44)( 25, 46)( 26, 45)( 27, 39)
( 28, 40)( 29, 42)( 30, 41)( 31, 47)( 32, 48)( 33, 50)( 34, 49)( 53, 54)
( 55, 59)( 56, 60)( 57, 62)( 58, 61)( 65, 66)( 67, 83)( 68, 84)( 69, 86)
( 70, 85)( 71, 91)( 72, 92)( 73, 94)( 74, 93)( 75, 87)( 76, 88)( 77, 90)
( 78, 89)( 79, 95)( 80, 96)( 81, 98)( 82, 97)( 99,147)(100,148)(101,150)
(102,149)(103,155)(104,156)(105,158)(106,157)(107,151)(108,152)(109,154)
(110,153)(111,159)(112,160)(113,162)(114,161)(115,179)(116,180)(117,182)
(118,181)(119,187)(120,188)(121,190)(122,189)(123,183)(124,184)(125,186)
(126,185)(127,191)(128,192)(129,194)(130,193)(131,163)(132,164)(133,166)
(134,165)(135,171)(136,172)(137,174)(138,173)(139,167)(140,168)(141,170)
(142,169)(143,175)(144,176)(145,178)(146,177);
s2 := Sym(194)!(  3,115)(  4,118)(  5,117)(  6,116)(  7,121)(  8,120)(  9,119)
( 10,122)( 11,128)( 12,129)( 13,130)( 14,127)( 15,126)( 16,123)( 17,124)
( 18,125)( 19, 99)( 20,102)( 21,101)( 22,100)( 23,105)( 24,104)( 25,103)
( 26,106)( 27,112)( 28,113)( 29,114)( 30,111)( 31,110)( 32,107)( 33,108)
( 34,109)( 35,131)( 36,134)( 37,133)( 38,132)( 39,137)( 40,136)( 41,135)
( 42,138)( 43,144)( 44,145)( 45,146)( 46,143)( 47,142)( 48,139)( 49,140)
( 50,141)( 51,163)( 52,166)( 53,165)( 54,164)( 55,169)( 56,168)( 57,167)
( 58,170)( 59,176)( 60,177)( 61,178)( 62,175)( 63,174)( 64,171)( 65,172)
( 66,173)( 67,147)( 68,150)( 69,149)( 70,148)( 71,153)( 72,152)( 73,151)
( 74,154)( 75,160)( 76,161)( 77,162)( 78,159)( 79,158)( 80,155)( 81,156)
( 82,157)( 83,179)( 84,182)( 85,181)( 86,180)( 87,185)( 88,184)( 89,183)
( 90,186)( 91,192)( 92,193)( 93,194)( 94,191)( 95,190)( 96,187)( 97,188)
( 98,189);
s3 := Sym(194)!(  3, 63)(  4, 64)(  5, 65)(  6, 66)(  7, 59)(  8, 60)(  9, 61)
( 10, 62)( 11, 55)( 12, 56)( 13, 57)( 14, 58)( 15, 51)( 16, 52)( 17, 53)
( 18, 54)( 19, 79)( 20, 80)( 21, 81)( 22, 82)( 23, 75)( 24, 76)( 25, 77)
( 26, 78)( 27, 71)( 28, 72)( 29, 73)( 30, 74)( 31, 67)( 32, 68)( 33, 69)
( 34, 70)( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 91)( 40, 92)( 41, 93)
( 42, 94)( 43, 87)( 44, 88)( 45, 89)( 46, 90)( 47, 83)( 48, 84)( 49, 85)
( 50, 86)( 99,159)(100,160)(101,161)(102,162)(103,155)(104,156)(105,157)
(106,158)(107,151)(108,152)(109,153)(110,154)(111,147)(112,148)(113,149)
(114,150)(115,175)(116,176)(117,177)(118,178)(119,171)(120,172)(121,173)
(122,174)(123,167)(124,168)(125,169)(126,170)(127,163)(128,164)(129,165)
(130,166)(131,191)(132,192)(133,193)(134,194)(135,187)(136,188)(137,189)
(138,190)(139,183)(140,184)(141,185)(142,186)(143,179)(144,180)(145,181)
(146,182);
poly := sub<Sym(194)|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,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;

to this polytope