Polytope of Type {22,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,6,6}*1584c
if this polytope has a name.
Group : SmallGroup(1584,675)
Rank : 4
Schlafli Type : {22,6,6}
Number of vertices, edges, etc : 22, 66, 18, 6
Order of s0s1s2s3 : 66
Order of s0s1s2s3s2s1 : 2
Special Properties :
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) :
3-fold quotients : {22,6,2}*528
9-fold quotients : {22,2,2}*176
11-fold quotients : {2,6,6}*144c
18-fold quotients : {11,2,2}*88
22-fold quotients : {2,3,6}*72
33-fold quotients : {2,6,2}*48
66-fold quotients : {2,3,2}*24
99-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)
( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)
( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)
( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)
( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)
(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)
(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)(137,140)
(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)(157,164)
(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)(171,172)
(178,187)(179,186)(180,185)(181,184)(182,183)(189,198)(190,197)(191,196)
(192,195)(193,194);;
s1 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 24)( 13, 23)( 14, 33)
( 15, 32)( 16, 31)( 17, 30)( 18, 29)( 19, 28)( 20, 27)( 21, 26)( 22, 25)
( 34, 68)( 35, 67)( 36, 77)( 37, 76)( 38, 75)( 39, 74)( 40, 73)( 41, 72)
( 42, 71)( 43, 70)( 44, 69)( 45, 90)( 46, 89)( 47, 99)( 48, 98)( 49, 97)
( 50, 96)( 51, 95)( 52, 94)( 53, 93)( 54, 92)( 55, 91)( 56, 79)( 57, 78)
( 58, 88)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 83)( 64, 82)( 65, 81)
( 66, 80)(100,101)(102,110)(103,109)(104,108)(105,107)(111,123)(112,122)
(113,132)(114,131)(115,130)(116,129)(117,128)(118,127)(119,126)(120,125)
(121,124)(133,167)(134,166)(135,176)(136,175)(137,174)(138,173)(139,172)
(140,171)(141,170)(142,169)(143,168)(144,189)(145,188)(146,198)(147,197)
(148,196)(149,195)(150,194)(151,193)(152,192)(153,191)(154,190)(155,178)
(156,177)(157,187)(158,186)(159,185)(160,184)(161,183)(162,182)(163,181)
(164,180)(165,179);;
s2 := ( 1,144)( 2,145)( 3,146)( 4,147)( 5,148)( 6,149)( 7,150)( 8,151)
( 9,152)( 10,153)( 11,154)( 12,133)( 13,134)( 14,135)( 15,136)( 16,137)
( 17,138)( 18,139)( 19,140)( 20,141)( 21,142)( 22,143)( 23,155)( 24,156)
( 25,157)( 26,158)( 27,159)( 28,160)( 29,161)( 30,162)( 31,163)( 32,164)
( 33,165)( 34,111)( 35,112)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)
( 41,118)( 42,119)( 43,120)( 44,121)( 45,100)( 46,101)( 47,102)( 48,103)
( 49,104)( 50,105)( 51,106)( 52,107)( 53,108)( 54,109)( 55,110)( 56,122)
( 57,123)( 58,124)( 59,125)( 60,126)( 61,127)( 62,128)( 63,129)( 64,130)
( 65,131)( 66,132)( 67,177)( 68,178)( 69,179)( 70,180)( 71,181)( 72,182)
( 73,183)( 74,184)( 75,185)( 76,186)( 77,187)( 78,166)( 79,167)( 80,168)
( 81,169)( 82,170)( 83,171)( 84,172)( 85,173)( 86,174)( 87,175)( 88,176)
( 89,188)( 90,189)( 91,190)( 92,191)( 93,192)( 94,193)( 95,194)( 96,195)
( 97,196)( 98,197)( 99,198);;
s3 := ( 12, 23)( 13, 24)( 14, 25)( 15, 26)( 16, 27)( 17, 28)( 18, 29)( 19, 30)
( 20, 31)( 21, 32)( 22, 33)( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)
( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 78, 89)( 79, 90)
( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)( 86, 97)( 87, 98)
( 88, 99)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)(117,128)
(118,129)(119,130)(120,131)(121,132)(144,155)(145,156)(146,157)(147,158)
(148,159)(149,160)(150,161)(151,162)(152,163)(153,164)(154,165)(177,188)
(178,189)(179,190)(180,191)(181,192)(182,193)(183,194)(184,195)(185,196)
(186,197)(187,198);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(198)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)
( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)
( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)
(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)
(123,132)(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)
(137,140)(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)
(157,164)(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)
(171,172)(178,187)(179,186)(180,185)(181,184)(182,183)(189,198)(190,197)
(191,196)(192,195)(193,194);
s1 := Sym(198)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 24)( 13, 23)
( 14, 33)( 15, 32)( 16, 31)( 17, 30)( 18, 29)( 19, 28)( 20, 27)( 21, 26)
( 22, 25)( 34, 68)( 35, 67)( 36, 77)( 37, 76)( 38, 75)( 39, 74)( 40, 73)
( 41, 72)( 42, 71)( 43, 70)( 44, 69)( 45, 90)( 46, 89)( 47, 99)( 48, 98)
( 49, 97)( 50, 96)( 51, 95)( 52, 94)( 53, 93)( 54, 92)( 55, 91)( 56, 79)
( 57, 78)( 58, 88)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 83)( 64, 82)
( 65, 81)( 66, 80)(100,101)(102,110)(103,109)(104,108)(105,107)(111,123)
(112,122)(113,132)(114,131)(115,130)(116,129)(117,128)(118,127)(119,126)
(120,125)(121,124)(133,167)(134,166)(135,176)(136,175)(137,174)(138,173)
(139,172)(140,171)(141,170)(142,169)(143,168)(144,189)(145,188)(146,198)
(147,197)(148,196)(149,195)(150,194)(151,193)(152,192)(153,191)(154,190)
(155,178)(156,177)(157,187)(158,186)(159,185)(160,184)(161,183)(162,182)
(163,181)(164,180)(165,179);
s2 := Sym(198)!( 1,144)( 2,145)( 3,146)( 4,147)( 5,148)( 6,149)( 7,150)
( 8,151)( 9,152)( 10,153)( 11,154)( 12,133)( 13,134)( 14,135)( 15,136)
( 16,137)( 17,138)( 18,139)( 19,140)( 20,141)( 21,142)( 22,143)( 23,155)
( 24,156)( 25,157)( 26,158)( 27,159)( 28,160)( 29,161)( 30,162)( 31,163)
( 32,164)( 33,165)( 34,111)( 35,112)( 36,113)( 37,114)( 38,115)( 39,116)
( 40,117)( 41,118)( 42,119)( 43,120)( 44,121)( 45,100)( 46,101)( 47,102)
( 48,103)( 49,104)( 50,105)( 51,106)( 52,107)( 53,108)( 54,109)( 55,110)
( 56,122)( 57,123)( 58,124)( 59,125)( 60,126)( 61,127)( 62,128)( 63,129)
( 64,130)( 65,131)( 66,132)( 67,177)( 68,178)( 69,179)( 70,180)( 71,181)
( 72,182)( 73,183)( 74,184)( 75,185)( 76,186)( 77,187)( 78,166)( 79,167)
( 80,168)( 81,169)( 82,170)( 83,171)( 84,172)( 85,173)( 86,174)( 87,175)
( 88,176)( 89,188)( 90,189)( 91,190)( 92,191)( 93,192)( 94,193)( 95,194)
( 96,195)( 97,196)( 98,197)( 99,198);
s3 := Sym(198)!( 12, 23)( 13, 24)( 14, 25)( 15, 26)( 16, 27)( 17, 28)( 18, 29)
( 19, 30)( 20, 31)( 21, 32)( 22, 33)( 45, 56)( 46, 57)( 47, 58)( 48, 59)
( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 78, 89)
( 79, 90)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)( 86, 97)
( 87, 98)( 88, 99)(111,122)(112,123)(113,124)(114,125)(115,126)(116,127)
(117,128)(118,129)(119,130)(120,131)(121,132)(144,155)(145,156)(146,157)
(147,158)(148,159)(149,160)(150,161)(151,162)(152,163)(153,164)(154,165)
(177,188)(178,189)(179,190)(180,191)(181,192)(182,193)(183,194)(184,195)
(185,196)(186,197)(187,198);
poly := sub<Sym(198)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope