Polytope of Type {2,6,32}

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

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

Permutation Representation (Magma) :

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

to this polytope