Polytope of Type {5,2,4,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,6,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240408)
Rank : 6
Schlafli Type : {5,2,4,6,4}
Number of vertices, edges, etc : 5, 5, 4, 12, 12, 4
Order of s0s1s2s3s4s5 : 30
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 : {5,2,4,3,4}*960
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 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)(196,197);;
s3 := ( 6,118)( 7,121)( 8,120)( 9,119)( 10,126)( 11,129)( 12,128)( 13,127)
( 14,122)( 15,125)( 16,124)( 17,123)( 18,130)( 19,133)( 20,132)( 21,131)
( 22,102)( 23,105)( 24,104)( 25,103)( 26,110)( 27,113)( 28,112)( 29,111)
( 30,106)( 31,109)( 32,108)( 33,107)( 34,114)( 35,117)( 36,116)( 37,115)
( 38,134)( 39,137)( 40,136)( 41,135)( 42,142)( 43,145)( 44,144)( 45,143)
( 46,138)( 47,141)( 48,140)( 49,139)( 50,146)( 51,149)( 52,148)( 53,147)
( 54,166)( 55,169)( 56,168)( 57,167)( 58,174)( 59,177)( 60,176)( 61,175)
( 62,170)( 63,173)( 64,172)( 65,171)( 66,178)( 67,181)( 68,180)( 69,179)
( 70,150)( 71,153)( 72,152)( 73,151)( 74,158)( 75,161)( 76,160)( 77,159)
( 78,154)( 79,157)( 80,156)( 81,155)( 82,162)( 83,165)( 84,164)( 85,163)
( 86,182)( 87,185)( 88,184)( 89,183)( 90,190)( 91,193)( 92,192)( 93,191)
( 94,186)( 95,189)( 96,188)( 97,187)( 98,194)( 99,197)(100,196)(101,195);;
s4 := ( 6,150)( 7,151)( 8,153)( 9,152)( 10,162)( 11,163)( 12,165)( 13,164)
( 14,158)( 15,159)( 16,161)( 17,160)( 18,154)( 19,155)( 20,157)( 21,156)
( 22,182)( 23,183)( 24,185)( 25,184)( 26,194)( 27,195)( 28,197)( 29,196)
( 30,190)( 31,191)( 32,193)( 33,192)( 34,186)( 35,187)( 36,189)( 37,188)
( 38,166)( 39,167)( 40,169)( 41,168)( 42,178)( 43,179)( 44,181)( 45,180)
( 46,174)( 47,175)( 48,177)( 49,176)( 50,170)( 51,171)( 52,173)( 53,172)
( 54,102)( 55,103)( 56,105)( 57,104)( 58,114)( 59,115)( 60,117)( 61,116)
( 62,110)( 63,111)( 64,113)( 65,112)( 66,106)( 67,107)( 68,109)( 69,108)
( 70,134)( 71,135)( 72,137)( 73,136)( 74,146)( 75,147)( 76,149)( 77,148)
( 78,142)( 79,143)( 80,145)( 81,144)( 82,138)( 83,139)( 84,141)( 85,140)
( 86,118)( 87,119)( 88,121)( 89,120)( 90,130)( 91,131)( 92,133)( 93,132)
( 94,126)( 95,127)( 96,129)( 97,128)( 98,122)( 99,123)(100,125)(101,124);;
s5 := ( 6, 18)( 7, 19)( 8, 20)( 9, 21)( 10, 14)( 11, 15)( 12, 16)( 13, 17)
( 22, 34)( 23, 35)( 24, 36)( 25, 37)( 26, 30)( 27, 31)( 28, 32)( 29, 33)
( 38, 50)( 39, 51)( 40, 52)( 41, 53)( 42, 46)( 43, 47)( 44, 48)( 45, 49)
( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 62)( 59, 63)( 60, 64)( 61, 65)
( 70, 82)( 71, 83)( 72, 84)( 73, 85)( 74, 78)( 75, 79)( 76, 80)( 77, 81)
( 86, 98)( 87, 99)( 88,100)( 89,101)( 90, 94)( 91, 95)( 92, 96)( 93, 97)
(102,114)(103,115)(104,116)(105,117)(106,110)(107,111)(108,112)(109,113)
(118,130)(119,131)(120,132)(121,133)(122,126)(123,127)(124,128)(125,129)
(134,146)(135,147)(136,148)(137,149)(138,142)(139,143)(140,144)(141,145)
(150,162)(151,163)(152,164)(153,165)(154,158)(155,159)(156,160)(157,161)
(166,178)(167,179)(168,180)(169,181)(170,174)(171,175)(172,176)(173,177)
(182,194)(183,195)(184,196)(185,197)(186,190)(187,191)(188,192)(189,193);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s2*s3,
s5*s4*s3*s5*s4*s5*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(197)!(2,3)(4,5);
s1 := Sym(197)!(1,2)(3,4);
s2 := Sym(197)!( 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)
(196,197);
s3 := Sym(197)!( 6,118)( 7,121)( 8,120)( 9,119)( 10,126)( 11,129)( 12,128)
( 13,127)( 14,122)( 15,125)( 16,124)( 17,123)( 18,130)( 19,133)( 20,132)
( 21,131)( 22,102)( 23,105)( 24,104)( 25,103)( 26,110)( 27,113)( 28,112)
( 29,111)( 30,106)( 31,109)( 32,108)( 33,107)( 34,114)( 35,117)( 36,116)
( 37,115)( 38,134)( 39,137)( 40,136)( 41,135)( 42,142)( 43,145)( 44,144)
( 45,143)( 46,138)( 47,141)( 48,140)( 49,139)( 50,146)( 51,149)( 52,148)
( 53,147)( 54,166)( 55,169)( 56,168)( 57,167)( 58,174)( 59,177)( 60,176)
( 61,175)( 62,170)( 63,173)( 64,172)( 65,171)( 66,178)( 67,181)( 68,180)
( 69,179)( 70,150)( 71,153)( 72,152)( 73,151)( 74,158)( 75,161)( 76,160)
( 77,159)( 78,154)( 79,157)( 80,156)( 81,155)( 82,162)( 83,165)( 84,164)
( 85,163)( 86,182)( 87,185)( 88,184)( 89,183)( 90,190)( 91,193)( 92,192)
( 93,191)( 94,186)( 95,189)( 96,188)( 97,187)( 98,194)( 99,197)(100,196)
(101,195);
s4 := Sym(197)!( 6,150)( 7,151)( 8,153)( 9,152)( 10,162)( 11,163)( 12,165)
( 13,164)( 14,158)( 15,159)( 16,161)( 17,160)( 18,154)( 19,155)( 20,157)
( 21,156)( 22,182)( 23,183)( 24,185)( 25,184)( 26,194)( 27,195)( 28,197)
( 29,196)( 30,190)( 31,191)( 32,193)( 33,192)( 34,186)( 35,187)( 36,189)
( 37,188)( 38,166)( 39,167)( 40,169)( 41,168)( 42,178)( 43,179)( 44,181)
( 45,180)( 46,174)( 47,175)( 48,177)( 49,176)( 50,170)( 51,171)( 52,173)
( 53,172)( 54,102)( 55,103)( 56,105)( 57,104)( 58,114)( 59,115)( 60,117)
( 61,116)( 62,110)( 63,111)( 64,113)( 65,112)( 66,106)( 67,107)( 68,109)
( 69,108)( 70,134)( 71,135)( 72,137)( 73,136)( 74,146)( 75,147)( 76,149)
( 77,148)( 78,142)( 79,143)( 80,145)( 81,144)( 82,138)( 83,139)( 84,141)
( 85,140)( 86,118)( 87,119)( 88,121)( 89,120)( 90,130)( 91,131)( 92,133)
( 93,132)( 94,126)( 95,127)( 96,129)( 97,128)( 98,122)( 99,123)(100,125)
(101,124);
s5 := Sym(197)!( 6, 18)( 7, 19)( 8, 20)( 9, 21)( 10, 14)( 11, 15)( 12, 16)
( 13, 17)( 22, 34)( 23, 35)( 24, 36)( 25, 37)( 26, 30)( 27, 31)( 28, 32)
( 29, 33)( 38, 50)( 39, 51)( 40, 52)( 41, 53)( 42, 46)( 43, 47)( 44, 48)
( 45, 49)( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 62)( 59, 63)( 60, 64)
( 61, 65)( 70, 82)( 71, 83)( 72, 84)( 73, 85)( 74, 78)( 75, 79)( 76, 80)
( 77, 81)( 86, 98)( 87, 99)( 88,100)( 89,101)( 90, 94)( 91, 95)( 92, 96)
( 93, 97)(102,114)(103,115)(104,116)(105,117)(106,110)(107,111)(108,112)
(109,113)(118,130)(119,131)(120,132)(121,133)(122,126)(123,127)(124,128)
(125,129)(134,146)(135,147)(136,148)(137,149)(138,142)(139,143)(140,144)
(141,145)(150,162)(151,163)(152,164)(153,165)(154,158)(155,159)(156,160)
(157,161)(166,178)(167,179)(168,180)(169,181)(170,174)(171,175)(172,176)
(173,177)(182,194)(183,195)(184,196)(185,197)(186,190)(187,191)(188,192)
(189,193);
poly := sub<Sym(197)|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,
s2*s3*s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5,
s2*s3*s4*s3*s2*s3*s4*s2*s3, s5*s4*s3*s5*s4*s5*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope