Polytope of Type {2,4,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,6}*768
if this polytope has a name.
Group : SmallGroup(768,1090146)
Rank : 5
Schlafli Type : {2,4,6,6}
Number of vertices, edges, etc : 2, 4, 16, 24, 8
Order of s0s1s2s3s4 : 4
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 : {2,4,6,3}*384, {2,2,6,6}*384
4-fold quotients : {2,2,3,6}*192, {2,2,6,3}*192
8-fold quotients : {2,2,3,3}*96
12-fold quotients : {2,4,2,2}*64
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, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)( 10, 58)
( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 63)( 16, 64)( 17, 65)( 18, 66)
( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)( 24, 72)( 25, 73)( 26, 74)
( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 33, 93)( 34, 94)
( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 75)( 40, 76)( 41, 77)( 42, 78)
( 43, 79)( 44, 80)( 45, 81)( 46, 82)( 47, 83)( 48, 84)( 49, 85)( 50, 86)
( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)(106,154)
(107,155)(108,156)(109,157)(110,158)(111,159)(112,160)(113,161)(114,162)
(115,163)(116,164)(117,165)(118,166)(119,167)(120,168)(121,169)(122,170)
(123,183)(124,184)(125,185)(126,186)(127,187)(128,188)(129,189)(130,190)
(131,191)(132,192)(133,193)(134,194)(135,171)(136,172)(137,173)(138,174)
(139,175)(140,176)(141,177)(142,178)(143,179)(144,180)(145,181)(146,182);;
s2 := ( 3, 27)( 4, 29)( 5, 28)( 6, 30)( 7, 35)( 8, 37)( 9, 36)( 10, 38)
( 11, 31)( 12, 33)( 13, 32)( 14, 34)( 15, 39)( 16, 41)( 17, 40)( 18, 42)
( 19, 47)( 20, 49)( 21, 48)( 22, 50)( 23, 43)( 24, 45)( 25, 44)( 26, 46)
( 51, 75)( 52, 77)( 53, 76)( 54, 78)( 55, 83)( 56, 85)( 57, 84)( 58, 86)
( 59, 79)( 60, 81)( 61, 80)( 62, 82)( 63, 87)( 64, 89)( 65, 88)( 66, 90)
( 67, 95)( 68, 97)( 69, 96)( 70, 98)( 71, 91)( 72, 93)( 73, 92)( 74, 94)
( 99,123)(100,125)(101,124)(102,126)(103,131)(104,133)(105,132)(106,134)
(107,127)(108,129)(109,128)(110,130)(111,135)(112,137)(113,136)(114,138)
(115,143)(116,145)(117,144)(118,146)(119,139)(120,141)(121,140)(122,142)
(147,171)(148,173)(149,172)(150,174)(151,179)(152,181)(153,180)(154,182)
(155,175)(156,177)(157,176)(158,178)(159,183)(160,185)(161,184)(162,186)
(163,191)(164,193)(165,192)(166,194)(167,187)(168,189)(169,188)(170,190);;
s3 := ( 3, 7)( 4, 8)( 5, 10)( 6, 9)( 13, 14)( 15, 19)( 16, 20)( 17, 22)
( 18, 21)( 25, 26)( 27, 31)( 28, 32)( 29, 34)( 30, 33)( 37, 38)( 39, 43)
( 40, 44)( 41, 46)( 42, 45)( 49, 50)( 51, 55)( 52, 56)( 53, 58)( 54, 57)
( 61, 62)( 63, 67)( 64, 68)( 65, 70)( 66, 69)( 73, 74)( 75, 79)( 76, 80)
( 77, 82)( 78, 81)( 85, 86)( 87, 91)( 88, 92)( 89, 94)( 90, 93)( 97, 98)
( 99,103)(100,104)(101,106)(102,105)(109,110)(111,115)(112,116)(113,118)
(114,117)(121,122)(123,127)(124,128)(125,130)(126,129)(133,134)(135,139)
(136,140)(137,142)(138,141)(145,146)(147,151)(148,152)(149,154)(150,153)
(157,158)(159,163)(160,164)(161,166)(162,165)(169,170)(171,175)(172,176)
(173,178)(174,177)(181,182)(183,187)(184,188)(185,190)(186,189)(193,194);;
s4 := ( 3,102)( 4,100)( 5,101)( 6, 99)( 7,110)( 8,108)( 9,109)( 10,107)
( 11,106)( 12,104)( 13,105)( 14,103)( 15,114)( 16,112)( 17,113)( 18,111)
( 19,122)( 20,120)( 21,121)( 22,119)( 23,118)( 24,116)( 25,117)( 26,115)
( 27,126)( 28,124)( 29,125)( 30,123)( 31,134)( 32,132)( 33,133)( 34,131)
( 35,130)( 36,128)( 37,129)( 38,127)( 39,138)( 40,136)( 41,137)( 42,135)
( 43,146)( 44,144)( 45,145)( 46,143)( 47,142)( 48,140)( 49,141)( 50,139)
( 51,150)( 52,148)( 53,149)( 54,147)( 55,158)( 56,156)( 57,157)( 58,155)
( 59,154)( 60,152)( 61,153)( 62,151)( 63,162)( 64,160)( 65,161)( 66,159)
( 67,170)( 68,168)( 69,169)( 70,167)( 71,166)( 72,164)( 73,165)( 74,163)
( 75,174)( 76,172)( 77,173)( 78,171)( 79,182)( 80,180)( 81,181)( 82,179)
( 83,178)( 84,176)( 85,177)( 86,175)( 87,186)( 88,184)( 89,185)( 90,183)
( 91,194)( 92,192)( 93,193)( 94,191)( 95,190)( 96,188)( 97,189)( 98,187);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 3, 51)( 4, 52)( 5, 53)( 6, 54)( 7, 55)( 8, 56)( 9, 57)
( 10, 58)( 11, 59)( 12, 60)( 13, 61)( 14, 62)( 15, 63)( 16, 64)( 17, 65)
( 18, 66)( 19, 67)( 20, 68)( 21, 69)( 22, 70)( 23, 71)( 24, 72)( 25, 73)
( 26, 74)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 33, 93)
( 34, 94)( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 75)( 40, 76)( 41, 77)
( 42, 78)( 43, 79)( 44, 80)( 45, 81)( 46, 82)( 47, 83)( 48, 84)( 49, 85)
( 50, 86)( 99,147)(100,148)(101,149)(102,150)(103,151)(104,152)(105,153)
(106,154)(107,155)(108,156)(109,157)(110,158)(111,159)(112,160)(113,161)
(114,162)(115,163)(116,164)(117,165)(118,166)(119,167)(120,168)(121,169)
(122,170)(123,183)(124,184)(125,185)(126,186)(127,187)(128,188)(129,189)
(130,190)(131,191)(132,192)(133,193)(134,194)(135,171)(136,172)(137,173)
(138,174)(139,175)(140,176)(141,177)(142,178)(143,179)(144,180)(145,181)
(146,182);
s2 := Sym(194)!( 3, 27)( 4, 29)( 5, 28)( 6, 30)( 7, 35)( 8, 37)( 9, 36)
( 10, 38)( 11, 31)( 12, 33)( 13, 32)( 14, 34)( 15, 39)( 16, 41)( 17, 40)
( 18, 42)( 19, 47)( 20, 49)( 21, 48)( 22, 50)( 23, 43)( 24, 45)( 25, 44)
( 26, 46)( 51, 75)( 52, 77)( 53, 76)( 54, 78)( 55, 83)( 56, 85)( 57, 84)
( 58, 86)( 59, 79)( 60, 81)( 61, 80)( 62, 82)( 63, 87)( 64, 89)( 65, 88)
( 66, 90)( 67, 95)( 68, 97)( 69, 96)( 70, 98)( 71, 91)( 72, 93)( 73, 92)
( 74, 94)( 99,123)(100,125)(101,124)(102,126)(103,131)(104,133)(105,132)
(106,134)(107,127)(108,129)(109,128)(110,130)(111,135)(112,137)(113,136)
(114,138)(115,143)(116,145)(117,144)(118,146)(119,139)(120,141)(121,140)
(122,142)(147,171)(148,173)(149,172)(150,174)(151,179)(152,181)(153,180)
(154,182)(155,175)(156,177)(157,176)(158,178)(159,183)(160,185)(161,184)
(162,186)(163,191)(164,193)(165,192)(166,194)(167,187)(168,189)(169,188)
(170,190);
s3 := Sym(194)!( 3, 7)( 4, 8)( 5, 10)( 6, 9)( 13, 14)( 15, 19)( 16, 20)
( 17, 22)( 18, 21)( 25, 26)( 27, 31)( 28, 32)( 29, 34)( 30, 33)( 37, 38)
( 39, 43)( 40, 44)( 41, 46)( 42, 45)( 49, 50)( 51, 55)( 52, 56)( 53, 58)
( 54, 57)( 61, 62)( 63, 67)( 64, 68)( 65, 70)( 66, 69)( 73, 74)( 75, 79)
( 76, 80)( 77, 82)( 78, 81)( 85, 86)( 87, 91)( 88, 92)( 89, 94)( 90, 93)
( 97, 98)( 99,103)(100,104)(101,106)(102,105)(109,110)(111,115)(112,116)
(113,118)(114,117)(121,122)(123,127)(124,128)(125,130)(126,129)(133,134)
(135,139)(136,140)(137,142)(138,141)(145,146)(147,151)(148,152)(149,154)
(150,153)(157,158)(159,163)(160,164)(161,166)(162,165)(169,170)(171,175)
(172,176)(173,178)(174,177)(181,182)(183,187)(184,188)(185,190)(186,189)
(193,194);
s4 := Sym(194)!( 3,102)( 4,100)( 5,101)( 6, 99)( 7,110)( 8,108)( 9,109)
( 10,107)( 11,106)( 12,104)( 13,105)( 14,103)( 15,114)( 16,112)( 17,113)
( 18,111)( 19,122)( 20,120)( 21,121)( 22,119)( 23,118)( 24,116)( 25,117)
( 26,115)( 27,126)( 28,124)( 29,125)( 30,123)( 31,134)( 32,132)( 33,133)
( 34,131)( 35,130)( 36,128)( 37,129)( 38,127)( 39,138)( 40,136)( 41,137)
( 42,135)( 43,146)( 44,144)( 45,145)( 46,143)( 47,142)( 48,140)( 49,141)
( 50,139)( 51,150)( 52,148)( 53,149)( 54,147)( 55,158)( 56,156)( 57,157)
( 58,155)( 59,154)( 60,152)( 61,153)( 62,151)( 63,162)( 64,160)( 65,161)
( 66,159)( 67,170)( 68,168)( 69,169)( 70,167)( 71,166)( 72,164)( 73,165)
( 74,163)( 75,174)( 76,172)( 77,173)( 78,171)( 79,182)( 80,180)( 81,181)
( 82,179)( 83,178)( 84,176)( 85,177)( 86,175)( 87,186)( 88,184)( 89,185)
( 90,183)( 91,194)( 92,192)( 93,193)( 94,191)( 95,190)( 96,188)( 97,189)
( 98,187);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 >;
to this polytope