Polytope of Type {2,4,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,4}*768b
if this polytope has a name.
Group : SmallGroup(768,1090146)
Rank : 5
Schlafli Type : {2,4,6,4}
Number of vertices, edges, etc : 2, 8, 24, 24, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
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 : {2,4,6,4}*384c, {2,4,6,2}*384
4-fold quotients : {2,2,6,4}*192a, {2,4,3,2}*192, {2,4,6,2}*192b, {2,4,6,2}*192c
8-fold quotients : {2,4,3,2}*96, {2,2,6,2}*96
12-fold quotients : {2,2,2,4}*64
16-fold quotients : {2,2,3,2}*48
24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,101)( 4,102)( 5, 99)( 6,100)( 7,105)( 8,106)( 9,103)( 10,104)
( 11,109)( 12,110)( 13,107)( 14,108)( 15,113)( 16,114)( 17,111)( 18,112)
( 19,117)( 20,118)( 21,115)( 22,116)( 23,121)( 24,122)( 25,119)( 26,120)
( 27,125)( 28,126)( 29,123)( 30,124)( 31,129)( 32,130)( 33,127)( 34,128)
( 35,133)( 36,134)( 37,131)( 38,132)( 39,137)( 40,138)( 41,135)( 42,136)
( 43,141)( 44,142)( 45,139)( 46,140)( 47,145)( 48,146)( 49,143)( 50,144)
( 51,149)( 52,150)( 53,147)( 54,148)( 55,153)( 56,154)( 57,151)( 58,152)
( 59,157)( 60,158)( 61,155)( 62,156)( 63,161)( 64,162)( 65,159)( 66,160)
( 67,165)( 68,166)( 69,163)( 70,164)( 71,169)( 72,170)( 73,167)( 74,168)
( 75,173)( 76,174)( 77,171)( 78,172)( 79,177)( 80,178)( 81,175)( 82,176)
( 83,181)( 84,182)( 85,179)( 86,180)( 87,185)( 88,186)( 89,183)( 90,184)
( 91,189)( 92,190)( 93,187)( 94,188)( 95,193)( 96,194)( 97,191)( 98,192);;
s2 := ( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 23)( 20, 25)
( 21, 24)( 22, 26)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 40, 41)
( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 52, 53)( 55, 59)( 56, 61)( 57, 60)
( 58, 62)( 64, 65)( 67, 71)( 68, 73)( 69, 72)( 70, 74)( 76, 77)( 79, 83)
( 80, 85)( 81, 84)( 82, 86)( 88, 89)( 91, 95)( 92, 97)( 93, 96)( 94, 98)
(100,101)(103,107)(104,109)(105,108)(106,110)(112,113)(115,119)(116,121)
(117,120)(118,122)(124,125)(127,131)(128,133)(129,132)(130,134)(136,137)
(139,143)(140,145)(141,144)(142,146)(148,149)(151,155)(152,157)(153,156)
(154,158)(160,161)(163,167)(164,169)(165,168)(166,170)(172,173)(175,179)
(176,181)(177,180)(178,182)(184,185)(187,191)(188,193)(189,192)(190,194);;
s3 := ( 3, 59)( 4, 62)( 5, 61)( 6, 60)( 7, 55)( 8, 58)( 9, 57)( 10, 56)
( 11, 51)( 12, 54)( 13, 53)( 14, 52)( 15, 71)( 16, 74)( 17, 73)( 18, 72)
( 19, 67)( 20, 70)( 21, 69)( 22, 68)( 23, 63)( 24, 66)( 25, 65)( 26, 64)
( 27, 95)( 28, 98)( 29, 97)( 30, 96)( 31, 91)( 32, 94)( 33, 93)( 34, 92)
( 35, 87)( 36, 90)( 37, 89)( 38, 88)( 39, 83)( 40, 86)( 41, 85)( 42, 84)
( 43, 79)( 44, 82)( 45, 81)( 46, 80)( 47, 75)( 48, 78)( 49, 77)( 50, 76)
( 99,155)(100,158)(101,157)(102,156)(103,151)(104,154)(105,153)(106,152)
(107,147)(108,150)(109,149)(110,148)(111,167)(112,170)(113,169)(114,168)
(115,163)(116,166)(117,165)(118,164)(119,159)(120,162)(121,161)(122,160)
(123,191)(124,194)(125,193)(126,192)(127,187)(128,190)(129,189)(130,188)
(131,183)(132,186)(133,185)(134,184)(135,179)(136,182)(137,181)(138,180)
(139,175)(140,178)(141,177)(142,176)(143,171)(144,174)(145,173)(146,172);;
s4 := ( 3, 27)( 4, 28)( 5, 29)( 6, 30)( 7, 31)( 8, 32)( 9, 33)( 10, 34)
( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)( 16, 40)( 17, 41)( 18, 42)
( 19, 43)( 20, 44)( 21, 45)( 22, 46)( 23, 47)( 24, 48)( 25, 49)( 26, 50)
( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)( 57, 81)( 58, 82)
( 59, 83)( 60, 84)( 61, 85)( 62, 86)( 63, 87)( 64, 88)( 65, 89)( 66, 90)
( 67, 91)( 68, 92)( 69, 93)( 70, 94)( 71, 95)( 72, 96)( 73, 97)( 74, 98)
( 99,123)(100,124)(101,125)(102,126)(103,127)(104,128)(105,129)(106,130)
(107,131)(108,132)(109,133)(110,134)(111,135)(112,136)(113,137)(114,138)
(115,139)(116,140)(117,141)(118,142)(119,143)(120,144)(121,145)(122,146)
(147,171)(148,172)(149,173)(150,174)(151,175)(152,176)(153,177)(154,178)
(155,179)(156,180)(157,181)(158,182)(159,183)(160,184)(161,185)(162,186)
(163,187)(164,188)(165,189)(166,190)(167,191)(168,192)(169,193)(170,194);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 3,101)( 4,102)( 5, 99)( 6,100)( 7,105)( 8,106)( 9,103)
( 10,104)( 11,109)( 12,110)( 13,107)( 14,108)( 15,113)( 16,114)( 17,111)
( 18,112)( 19,117)( 20,118)( 21,115)( 22,116)( 23,121)( 24,122)( 25,119)
( 26,120)( 27,125)( 28,126)( 29,123)( 30,124)( 31,129)( 32,130)( 33,127)
( 34,128)( 35,133)( 36,134)( 37,131)( 38,132)( 39,137)( 40,138)( 41,135)
( 42,136)( 43,141)( 44,142)( 45,139)( 46,140)( 47,145)( 48,146)( 49,143)
( 50,144)( 51,149)( 52,150)( 53,147)( 54,148)( 55,153)( 56,154)( 57,151)
( 58,152)( 59,157)( 60,158)( 61,155)( 62,156)( 63,161)( 64,162)( 65,159)
( 66,160)( 67,165)( 68,166)( 69,163)( 70,164)( 71,169)( 72,170)( 73,167)
( 74,168)( 75,173)( 76,174)( 77,171)( 78,172)( 79,177)( 80,178)( 81,175)
( 82,176)( 83,181)( 84,182)( 85,179)( 86,180)( 87,185)( 88,186)( 89,183)
( 90,184)( 91,189)( 92,190)( 93,187)( 94,188)( 95,193)( 96,194)( 97,191)
( 98,192);
s2 := Sym(194)!( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 23)
( 20, 25)( 21, 24)( 22, 26)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)
( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 52, 53)( 55, 59)( 56, 61)
( 57, 60)( 58, 62)( 64, 65)( 67, 71)( 68, 73)( 69, 72)( 70, 74)( 76, 77)
( 79, 83)( 80, 85)( 81, 84)( 82, 86)( 88, 89)( 91, 95)( 92, 97)( 93, 96)
( 94, 98)(100,101)(103,107)(104,109)(105,108)(106,110)(112,113)(115,119)
(116,121)(117,120)(118,122)(124,125)(127,131)(128,133)(129,132)(130,134)
(136,137)(139,143)(140,145)(141,144)(142,146)(148,149)(151,155)(152,157)
(153,156)(154,158)(160,161)(163,167)(164,169)(165,168)(166,170)(172,173)
(175,179)(176,181)(177,180)(178,182)(184,185)(187,191)(188,193)(189,192)
(190,194);
s3 := Sym(194)!( 3, 59)( 4, 62)( 5, 61)( 6, 60)( 7, 55)( 8, 58)( 9, 57)
( 10, 56)( 11, 51)( 12, 54)( 13, 53)( 14, 52)( 15, 71)( 16, 74)( 17, 73)
( 18, 72)( 19, 67)( 20, 70)( 21, 69)( 22, 68)( 23, 63)( 24, 66)( 25, 65)
( 26, 64)( 27, 95)( 28, 98)( 29, 97)( 30, 96)( 31, 91)( 32, 94)( 33, 93)
( 34, 92)( 35, 87)( 36, 90)( 37, 89)( 38, 88)( 39, 83)( 40, 86)( 41, 85)
( 42, 84)( 43, 79)( 44, 82)( 45, 81)( 46, 80)( 47, 75)( 48, 78)( 49, 77)
( 50, 76)( 99,155)(100,158)(101,157)(102,156)(103,151)(104,154)(105,153)
(106,152)(107,147)(108,150)(109,149)(110,148)(111,167)(112,170)(113,169)
(114,168)(115,163)(116,166)(117,165)(118,164)(119,159)(120,162)(121,161)
(122,160)(123,191)(124,194)(125,193)(126,192)(127,187)(128,190)(129,189)
(130,188)(131,183)(132,186)(133,185)(134,184)(135,179)(136,182)(137,181)
(138,180)(139,175)(140,178)(141,177)(142,176)(143,171)(144,174)(145,173)
(146,172);
s4 := Sym(194)!( 3, 27)( 4, 28)( 5, 29)( 6, 30)( 7, 31)( 8, 32)( 9, 33)
( 10, 34)( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)( 16, 40)( 17, 41)
( 18, 42)( 19, 43)( 20, 44)( 21, 45)( 22, 46)( 23, 47)( 24, 48)( 25, 49)
( 26, 50)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)( 57, 81)
( 58, 82)( 59, 83)( 60, 84)( 61, 85)( 62, 86)( 63, 87)( 64, 88)( 65, 89)
( 66, 90)( 67, 91)( 68, 92)( 69, 93)( 70, 94)( 71, 95)( 72, 96)( 73, 97)
( 74, 98)( 99,123)(100,124)(101,125)(102,126)(103,127)(104,128)(105,129)
(106,130)(107,131)(108,132)(109,133)(110,134)(111,135)(112,136)(113,137)
(114,138)(115,139)(116,140)(117,141)(118,142)(119,143)(120,144)(121,145)
(122,146)(147,171)(148,172)(149,173)(150,174)(151,175)(152,176)(153,177)
(154,178)(155,179)(156,180)(157,181)(158,182)(159,183)(160,184)(161,185)
(162,186)(163,187)(164,188)(165,189)(166,190)(167,191)(168,192)(169,193)
(170,194);
poly := sub<Sym(194)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope