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}*1920b
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, 8, 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
4-fold quotients : {5,2,2,3,4}*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, 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)( 52,101)( 53,100)
(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)(148,197)(149,196);;
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, 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, 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, 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, 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)( 52,101)
( 53,100)(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)(148,197)
(149,196);
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, 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,
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope