Polytope of Type {2,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*768b
if this polytope has a name.
Group : SmallGroup(768,1089114)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 16, 96, 16
Order of s₀s₁s₂s₃ : 8
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 : {2,6,12}*384b, {2,12,6}*384b
   4-fold quotients : {2,3,12}*192, {2,12,3}*192, {2,6,6}*192
   8-fold quotients : {2,3,6}*96, {2,6,3}*96
   16-fold quotients : {2,3,3}*48
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope