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