Polytope of Type {5,2,4,3,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,3,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240408)
Rank : 6
Schlafli Type : {5,2,4,3,4}
Number of vertices, edges, etc : 5, 5, 4, 12, 12, 8
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
4-fold quotients : {5,2,4,3,2}*480
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 := ( 6,102)( 7,103)( 8,105)( 9,104)( 10,114)( 11,115)( 12,117)( 13,116)
( 14,110)( 15,111)( 16,113)( 17,112)( 18,106)( 19,107)( 20,109)( 21,108)
( 22,134)( 23,135)( 24,137)( 25,136)( 26,146)( 27,147)( 28,149)( 29,148)
( 30,142)( 31,143)( 32,145)( 33,144)( 34,138)( 35,139)( 36,141)( 37,140)
( 38,118)( 39,119)( 40,121)( 41,120)( 42,130)( 43,131)( 44,133)( 45,132)
( 46,126)( 47,127)( 48,129)( 49,128)( 50,122)( 51,123)( 52,125)( 53,124)
( 54,150)( 55,151)( 56,153)( 57,152)( 58,162)( 59,163)( 60,165)( 61,164)
( 62,158)( 63,159)( 64,161)( 65,160)( 66,154)( 67,155)( 68,157)( 69,156)
( 70,182)( 71,183)( 72,185)( 73,184)( 74,194)( 75,195)( 76,197)( 77,196)
( 78,190)( 79,191)( 80,193)( 81,192)( 82,186)( 83,187)( 84,189)( 85,188)
( 86,166)( 87,167)( 88,169)( 89,168)( 90,178)( 91,179)( 92,181)( 93,180)
( 94,174)( 95,175)( 96,177)( 97,176)( 98,170)( 99,171)(100,173)(101,172);;
s5 := ( 6, 66)( 7, 67)( 8, 68)( 9, 69)( 10, 62)( 11, 63)( 12, 64)( 13, 65)
( 14, 58)( 15, 59)( 16, 60)( 17, 61)( 18, 54)( 19, 55)( 20, 56)( 21, 57)
( 22, 82)( 23, 83)( 24, 84)( 25, 85)( 26, 78)( 27, 79)( 28, 80)( 29, 81)
( 30, 74)( 31, 75)( 32, 76)( 33, 77)( 34, 70)( 35, 71)( 36, 72)( 37, 73)
( 38, 98)( 39, 99)( 40,100)( 41,101)( 42, 94)( 43, 95)( 44, 96)( 45, 97)
( 46, 90)( 47, 91)( 48, 92)( 49, 93)( 50, 86)( 51, 87)( 52, 88)( 53, 89)
(102,162)(103,163)(104,164)(105,165)(106,158)(107,159)(108,160)(109,161)
(110,154)(111,155)(112,156)(113,157)(114,150)(115,151)(116,152)(117,153)
(118,178)(119,179)(120,180)(121,181)(122,174)(123,175)(124,176)(125,177)
(126,170)(127,171)(128,172)(129,173)(130,166)(131,167)(132,168)(133,169)
(134,194)(135,195)(136,196)(137,197)(138,190)(139,191)(140,192)(141,193)
(142,186)(143,187)(144,188)(145,189)(146,182)(147,183)(148,184)(149,185);;
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, 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
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)!( 6,102)( 7,103)( 8,105)( 9,104)( 10,114)( 11,115)( 12,117)
( 13,116)( 14,110)( 15,111)( 16,113)( 17,112)( 18,106)( 19,107)( 20,109)
( 21,108)( 22,134)( 23,135)( 24,137)( 25,136)( 26,146)( 27,147)( 28,149)
( 29,148)( 30,142)( 31,143)( 32,145)( 33,144)( 34,138)( 35,139)( 36,141)
( 37,140)( 38,118)( 39,119)( 40,121)( 41,120)( 42,130)( 43,131)( 44,133)
( 45,132)( 46,126)( 47,127)( 48,129)( 49,128)( 50,122)( 51,123)( 52,125)
( 53,124)( 54,150)( 55,151)( 56,153)( 57,152)( 58,162)( 59,163)( 60,165)
( 61,164)( 62,158)( 63,159)( 64,161)( 65,160)( 66,154)( 67,155)( 68,157)
( 69,156)( 70,182)( 71,183)( 72,185)( 73,184)( 74,194)( 75,195)( 76,197)
( 77,196)( 78,190)( 79,191)( 80,193)( 81,192)( 82,186)( 83,187)( 84,189)
( 85,188)( 86,166)( 87,167)( 88,169)( 89,168)( 90,178)( 91,179)( 92,181)
( 93,180)( 94,174)( 95,175)( 96,177)( 97,176)( 98,170)( 99,171)(100,173)
(101,172);
s5 := Sym(197)!( 6, 66)( 7, 67)( 8, 68)( 9, 69)( 10, 62)( 11, 63)( 12, 64)
( 13, 65)( 14, 58)( 15, 59)( 16, 60)( 17, 61)( 18, 54)( 19, 55)( 20, 56)
( 21, 57)( 22, 82)( 23, 83)( 24, 84)( 25, 85)( 26, 78)( 27, 79)( 28, 80)
( 29, 81)( 30, 74)( 31, 75)( 32, 76)( 33, 77)( 34, 70)( 35, 71)( 36, 72)
( 37, 73)( 38, 98)( 39, 99)( 40,100)( 41,101)( 42, 94)( 43, 95)( 44, 96)
( 45, 97)( 46, 90)( 47, 91)( 48, 92)( 49, 93)( 50, 86)( 51, 87)( 52, 88)
( 53, 89)(102,162)(103,163)(104,164)(105,165)(106,158)(107,159)(108,160)
(109,161)(110,154)(111,155)(112,156)(113,157)(114,150)(115,151)(116,152)
(117,153)(118,178)(119,179)(120,180)(121,181)(122,174)(123,175)(124,176)
(125,177)(126,170)(127,171)(128,172)(129,173)(130,166)(131,167)(132,168)
(133,169)(134,194)(135,195)(136,196)(137,197)(138,190)(139,191)(140,192)
(141,193)(142,186)(143,187)(144,188)(145,189)(146,182)(147,183)(148,184)
(149,185);
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,
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope