Polytope of Type {3,2,4,3,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,3,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157864)
Rank : 6
Schlafli Type : {3,2,4,3,4}
Number of vertices, edges, etc : 3, 3, 4, 12, 12, 8
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {3,2,4,3,4}*576
4-fold quotients : {3,2,4,3,2}*288
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4, 5)( 6, 7)( 8, 9)( 10, 11)( 12, 13)( 14, 15)( 16, 17)( 18, 19)
( 20, 21)( 22, 23)( 24, 25)( 26, 27)( 28, 29)( 30, 31)( 32, 33)( 34, 35)
( 36, 37)( 38, 39)( 40, 41)( 42, 43)( 44, 45)( 46, 47)( 48, 49)( 50, 51)
( 52, 53)( 54, 55)( 56, 57)( 58, 59)( 60, 61)( 62, 63)( 64, 65)( 66, 67)
( 68, 69)( 70, 71)( 72, 73)( 74, 75)( 76, 77)( 78, 79)( 80, 81)( 82, 83)
( 84, 85)( 86, 87)( 88, 89)( 90, 91)( 92, 93)( 94, 95)( 96, 97)( 98, 99)
(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)
(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)(128,129)(130,131)
(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)(146,147)
(148,149)(150,151)(152,153)(154,155)(156,157)(158,159)(160,161)(162,163)
(164,165)(166,167)(168,169)(170,171)(172,173)(174,175)(176,177)(178,179)
(180,181)(182,183)(184,185)(186,187)(188,189)(190,191)(192,193)(194,195);;
s3 := ( 4,116)( 5,119)( 6,118)( 7,117)( 8,124)( 9,127)( 10,126)( 11,125)
( 12,120)( 13,123)( 14,122)( 15,121)( 16,128)( 17,131)( 18,130)( 19,129)
( 20,100)( 21,103)( 22,102)( 23,101)( 24,108)( 25,111)( 26,110)( 27,109)
( 28,104)( 29,107)( 30,106)( 31,105)( 32,112)( 33,115)( 34,114)( 35,113)
( 36,132)( 37,135)( 38,134)( 39,133)( 40,140)( 41,143)( 42,142)( 43,141)
( 44,136)( 45,139)( 46,138)( 47,137)( 48,144)( 49,147)( 50,146)( 51,145)
( 52,164)( 53,167)( 54,166)( 55,165)( 56,172)( 57,175)( 58,174)( 59,173)
( 60,168)( 61,171)( 62,170)( 63,169)( 64,176)( 65,179)( 66,178)( 67,177)
( 68,148)( 69,151)( 70,150)( 71,149)( 72,156)( 73,159)( 74,158)( 75,157)
( 76,152)( 77,155)( 78,154)( 79,153)( 80,160)( 81,163)( 82,162)( 83,161)
( 84,180)( 85,183)( 86,182)( 87,181)( 88,188)( 89,191)( 90,190)( 91,189)
( 92,184)( 93,187)( 94,186)( 95,185)( 96,192)( 97,195)( 98,194)( 99,193);;
s4 := ( 4,100)( 5,101)( 6,103)( 7,102)( 8,112)( 9,113)( 10,115)( 11,114)
( 12,108)( 13,109)( 14,111)( 15,110)( 16,104)( 17,105)( 18,107)( 19,106)
( 20,132)( 21,133)( 22,135)( 23,134)( 24,144)( 25,145)( 26,147)( 27,146)
( 28,140)( 29,141)( 30,143)( 31,142)( 32,136)( 33,137)( 34,139)( 35,138)
( 36,116)( 37,117)( 38,119)( 39,118)( 40,128)( 41,129)( 42,131)( 43,130)
( 44,124)( 45,125)( 46,127)( 47,126)( 48,120)( 49,121)( 50,123)( 51,122)
( 52,148)( 53,149)( 54,151)( 55,150)( 56,160)( 57,161)( 58,163)( 59,162)
( 60,156)( 61,157)( 62,159)( 63,158)( 64,152)( 65,153)( 66,155)( 67,154)
( 68,180)( 69,181)( 70,183)( 71,182)( 72,192)( 73,193)( 74,195)( 75,194)
( 76,188)( 77,189)( 78,191)( 79,190)( 80,184)( 81,185)( 82,187)( 83,186)
( 84,164)( 85,165)( 86,167)( 87,166)( 88,176)( 89,177)( 90,179)( 91,178)
( 92,172)( 93,173)( 94,175)( 95,174)( 96,168)( 97,169)( 98,171)( 99,170);;
s5 := ( 4, 64)( 5, 65)( 6, 66)( 7, 67)( 8, 60)( 9, 61)( 10, 62)( 11, 63)
( 12, 56)( 13, 57)( 14, 58)( 15, 59)( 16, 52)( 17, 53)( 18, 54)( 19, 55)
( 20, 80)( 21, 81)( 22, 82)( 23, 83)( 24, 76)( 25, 77)( 26, 78)( 27, 79)
( 28, 72)( 29, 73)( 30, 74)( 31, 75)( 32, 68)( 33, 69)( 34, 70)( 35, 71)
( 36, 96)( 37, 97)( 38, 98)( 39, 99)( 40, 92)( 41, 93)( 42, 94)( 43, 95)
( 44, 88)( 45, 89)( 46, 90)( 47, 91)( 48, 84)( 49, 85)( 50, 86)( 51, 87)
(100,160)(101,161)(102,162)(103,163)(104,156)(105,157)(106,158)(107,159)
(108,152)(109,153)(110,154)(111,155)(112,148)(113,149)(114,150)(115,151)
(116,176)(117,177)(118,178)(119,179)(120,172)(121,173)(122,174)(123,175)
(124,168)(125,169)(126,170)(127,171)(128,164)(129,165)(130,166)(131,167)
(132,192)(133,193)(134,194)(135,195)(136,188)(137,189)(138,190)(139,191)
(140,184)(141,185)(142,186)(143,187)(144,180)(145,181)(146,182)(147,183);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5*s4*s5, s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(195)!(2,3);
s1 := Sym(195)!(1,2);
s2 := Sym(195)!( 4, 5)( 6, 7)( 8, 9)( 10, 11)( 12, 13)( 14, 15)( 16, 17)
( 18, 19)( 20, 21)( 22, 23)( 24, 25)( 26, 27)( 28, 29)( 30, 31)( 32, 33)
( 34, 35)( 36, 37)( 38, 39)( 40, 41)( 42, 43)( 44, 45)( 46, 47)( 48, 49)
( 50, 51)( 52, 53)( 54, 55)( 56, 57)( 58, 59)( 60, 61)( 62, 63)( 64, 65)
( 66, 67)( 68, 69)( 70, 71)( 72, 73)( 74, 75)( 76, 77)( 78, 79)( 80, 81)
( 82, 83)( 84, 85)( 86, 87)( 88, 89)( 90, 91)( 92, 93)( 94, 95)( 96, 97)
( 98, 99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)
(114,115)(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)(128,129)
(130,131)(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)
(146,147)(148,149)(150,151)(152,153)(154,155)(156,157)(158,159)(160,161)
(162,163)(164,165)(166,167)(168,169)(170,171)(172,173)(174,175)(176,177)
(178,179)(180,181)(182,183)(184,185)(186,187)(188,189)(190,191)(192,193)
(194,195);
s3 := Sym(195)!( 4,116)( 5,119)( 6,118)( 7,117)( 8,124)( 9,127)( 10,126)
( 11,125)( 12,120)( 13,123)( 14,122)( 15,121)( 16,128)( 17,131)( 18,130)
( 19,129)( 20,100)( 21,103)( 22,102)( 23,101)( 24,108)( 25,111)( 26,110)
( 27,109)( 28,104)( 29,107)( 30,106)( 31,105)( 32,112)( 33,115)( 34,114)
( 35,113)( 36,132)( 37,135)( 38,134)( 39,133)( 40,140)( 41,143)( 42,142)
( 43,141)( 44,136)( 45,139)( 46,138)( 47,137)( 48,144)( 49,147)( 50,146)
( 51,145)( 52,164)( 53,167)( 54,166)( 55,165)( 56,172)( 57,175)( 58,174)
( 59,173)( 60,168)( 61,171)( 62,170)( 63,169)( 64,176)( 65,179)( 66,178)
( 67,177)( 68,148)( 69,151)( 70,150)( 71,149)( 72,156)( 73,159)( 74,158)
( 75,157)( 76,152)( 77,155)( 78,154)( 79,153)( 80,160)( 81,163)( 82,162)
( 83,161)( 84,180)( 85,183)( 86,182)( 87,181)( 88,188)( 89,191)( 90,190)
( 91,189)( 92,184)( 93,187)( 94,186)( 95,185)( 96,192)( 97,195)( 98,194)
( 99,193);
s4 := Sym(195)!( 4,100)( 5,101)( 6,103)( 7,102)( 8,112)( 9,113)( 10,115)
( 11,114)( 12,108)( 13,109)( 14,111)( 15,110)( 16,104)( 17,105)( 18,107)
( 19,106)( 20,132)( 21,133)( 22,135)( 23,134)( 24,144)( 25,145)( 26,147)
( 27,146)( 28,140)( 29,141)( 30,143)( 31,142)( 32,136)( 33,137)( 34,139)
( 35,138)( 36,116)( 37,117)( 38,119)( 39,118)( 40,128)( 41,129)( 42,131)
( 43,130)( 44,124)( 45,125)( 46,127)( 47,126)( 48,120)( 49,121)( 50,123)
( 51,122)( 52,148)( 53,149)( 54,151)( 55,150)( 56,160)( 57,161)( 58,163)
( 59,162)( 60,156)( 61,157)( 62,159)( 63,158)( 64,152)( 65,153)( 66,155)
( 67,154)( 68,180)( 69,181)( 70,183)( 71,182)( 72,192)( 73,193)( 74,195)
( 75,194)( 76,188)( 77,189)( 78,191)( 79,190)( 80,184)( 81,185)( 82,187)
( 83,186)( 84,164)( 85,165)( 86,167)( 87,166)( 88,176)( 89,177)( 90,179)
( 91,178)( 92,172)( 93,173)( 94,175)( 95,174)( 96,168)( 97,169)( 98,171)
( 99,170);
s5 := Sym(195)!( 4, 64)( 5, 65)( 6, 66)( 7, 67)( 8, 60)( 9, 61)( 10, 62)
( 11, 63)( 12, 56)( 13, 57)( 14, 58)( 15, 59)( 16, 52)( 17, 53)( 18, 54)
( 19, 55)( 20, 80)( 21, 81)( 22, 82)( 23, 83)( 24, 76)( 25, 77)( 26, 78)
( 27, 79)( 28, 72)( 29, 73)( 30, 74)( 31, 75)( 32, 68)( 33, 69)( 34, 70)
( 35, 71)( 36, 96)( 37, 97)( 38, 98)( 39, 99)( 40, 92)( 41, 93)( 42, 94)
( 43, 95)( 44, 88)( 45, 89)( 46, 90)( 47, 91)( 48, 84)( 49, 85)( 50, 86)
( 51, 87)(100,160)(101,161)(102,162)(103,163)(104,156)(105,157)(106,158)
(107,159)(108,152)(109,153)(110,154)(111,155)(112,148)(113,149)(114,150)
(115,151)(116,176)(117,177)(118,178)(119,179)(120,172)(121,173)(122,174)
(123,175)(124,168)(125,169)(126,170)(127,171)(128,164)(129,165)(130,166)
(131,167)(132,192)(133,193)(134,194)(135,195)(136,188)(137,189)(138,190)
(139,191)(140,184)(141,185)(142,186)(143,187)(144,180)(145,181)(146,182)
(147,183);
poly := sub<Sym(195)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5,
s4*s2*s3*s4*s2*s3*s4*s2*s3 >;
to this polytope