Polytope of Type {12,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8,2}*768e
if this polytope has a name.
Group : SmallGroup(768,1089114)
Rank : 4
Schlafli Type : {12,8,2}
Number of vertices, edges, etc : 24, 96, 16, 2
Order of s₀s₁s₂s₃ : 12
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 : {12,4,2}*384b, {6,8,2}*384b
   4-fold quotients : {12,4,2}*192b, {12,4,2}*192c, {3,8,2}*192, {6,4,2}*192
   8-fold quotients : {12,2,2}*96, {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   16-fold quotients : {3,4,2}*48, {6,2,2}*48
   24-fold quotients : {4,2,2}*32
   32-fold quotients : {3,2,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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, 53)(  4, 54)(  5, 52)(  6, 51)(  7, 50)(  8, 49)
(  9, 63)( 10, 64)( 11, 61)( 12, 62)( 13, 60)( 14, 59)( 15, 58)( 16, 57)
( 17, 71)( 18, 72)( 19, 69)( 20, 70)( 21, 68)( 22, 67)( 23, 66)( 24, 65)
( 25, 79)( 26, 80)( 27, 77)( 28, 78)( 29, 76)( 30, 75)( 31, 74)( 32, 73)
( 33, 87)( 34, 88)( 35, 85)( 36, 86)( 37, 84)( 38, 83)( 39, 82)( 40, 81)
( 41, 95)( 42, 96)( 43, 93)( 44, 94)( 45, 92)( 46, 91)( 47, 90)( 48, 89)
( 97,151)( 98,152)( 99,149)(100,150)(101,148)(102,147)(103,146)(104,145)
(105,159)(106,160)(107,157)(108,158)(109,156)(110,155)(111,154)(112,153)
(113,167)(114,168)(115,165)(116,166)(117,164)(118,163)(119,162)(120,161)
(121,175)(122,176)(123,173)(124,174)(125,172)(126,171)(127,170)(128,169)
(129,183)(130,184)(131,181)(132,182)(133,180)(134,179)(135,178)(136,177)
(137,191)(138,192)(139,189)(140,190)(141,188)(142,187)(143,186)(144,185);;
s3 := (193,194);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*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(194)!(  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(194)!(  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(194)!(  1, 55)(  2, 56)(  3, 53)(  4, 54)(  5, 52)(  6, 51)(  7, 50)
(  8, 49)(  9, 63)( 10, 64)( 11, 61)( 12, 62)( 13, 60)( 14, 59)( 15, 58)
( 16, 57)( 17, 71)( 18, 72)( 19, 69)( 20, 70)( 21, 68)( 22, 67)( 23, 66)
( 24, 65)( 25, 79)( 26, 80)( 27, 77)( 28, 78)( 29, 76)( 30, 75)( 31, 74)
( 32, 73)( 33, 87)( 34, 88)( 35, 85)( 36, 86)( 37, 84)( 38, 83)( 39, 82)
( 40, 81)( 41, 95)( 42, 96)( 43, 93)( 44, 94)( 45, 92)( 46, 91)( 47, 90)
( 48, 89)( 97,151)( 98,152)( 99,149)(100,150)(101,148)(102,147)(103,146)
(104,145)(105,159)(106,160)(107,157)(108,158)(109,156)(110,155)(111,154)
(112,153)(113,167)(114,168)(115,165)(116,166)(117,164)(118,163)(119,162)
(120,161)(121,175)(122,176)(123,173)(124,174)(125,172)(126,171)(127,170)
(128,169)(129,183)(130,184)(131,181)(132,182)(133,180)(134,179)(135,178)
(136,177)(137,191)(138,192)(139,189)(140,190)(141,188)(142,187)(143,186)
(144,185);
s3 := Sym(194)!(193,194);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*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 >;

to this polytope