Polytope of Type {2,32,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,32,6}*768
if this polytope has a name.
Group : SmallGroup(768,327682)
Rank : 4
Schlafli Type : {2,32,6}
Number of vertices, edges, etc : 2, 32, 96, 6
Order of s₀s₁s₂s₃ : 96
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 : {2,16,6}*384
   3-fold quotients : {2,32,2}*256
   4-fold quotients : {2,8,6}*192
   6-fold quotients : {2,16,2}*128
   8-fold quotients : {2,4,6}*96a
   12-fold quotients : {2,8,2}*64
   16-fold quotients : {2,2,6}*48
   24-fold quotients : {2,4,2}*32
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope