Polytope of Type {22,10,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,10,4}*1760
Also Known As : {{22,10|2},{10,4|2}}. if this polytope has another name.
Group : SmallGroup(1760,1190)
Rank : 4
Schlafli Type : {22,10,4}
Number of vertices, edges, etc : 22, 110, 20, 4
Order of s0s1s2s3 : 220
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) :
2-fold quotients : {22,10,2}*880
5-fold quotients : {22,2,4}*352
10-fold quotients : {11,2,4}*176, {22,2,2}*176
11-fold quotients : {2,10,4}*160
20-fold quotients : {11,2,2}*88
22-fold quotients : {2,10,2}*80
44-fold quotients : {2,5,2}*40
55-fold quotients : {2,2,4}*32
110-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)(200,209)(201,208)(202,207)(203,206)(204,205)(211,220)
(212,219)(213,218)(214,217)(215,216);;
s1 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 46)( 13, 45)( 14, 55)
( 15, 54)( 16, 53)( 17, 52)( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)
( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)
( 31, 38)( 32, 37)( 33, 36)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)
( 67,101)( 68,100)( 69,110)( 70,109)( 71,108)( 72,107)( 73,106)( 74,105)
( 75,104)( 76,103)( 77,102)( 78, 90)( 79, 89)( 80, 99)( 81, 98)( 82, 97)
( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)( 88, 91)(111,112)(113,121)
(114,120)(115,119)(116,118)(122,156)(123,155)(124,165)(125,164)(126,163)
(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,145)(134,144)
(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)(142,147)
(143,146)(166,167)(168,176)(169,175)(170,174)(171,173)(177,211)(178,210)
(179,220)(180,219)(181,218)(182,217)(183,216)(184,215)(185,214)(186,213)
(187,212)(188,200)(189,199)(190,209)(191,208)(192,207)(193,206)(194,205)
(195,204)(196,203)(197,202)(198,201);;
s2 := ( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 16)( 6, 17)( 7, 18)( 8, 19)
( 9, 20)( 10, 21)( 11, 22)( 23, 45)( 24, 46)( 25, 47)( 26, 48)( 27, 49)
( 28, 50)( 29, 51)( 30, 52)( 31, 53)( 32, 54)( 33, 55)( 56, 67)( 57, 68)
( 58, 69)( 59, 70)( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)( 65, 76)
( 66, 77)( 78,100)( 79,101)( 80,102)( 81,103)( 82,104)( 83,105)( 84,106)
( 85,107)( 86,108)( 87,109)( 88,110)(111,177)(112,178)(113,179)(114,180)
(115,181)(116,182)(117,183)(118,184)(119,185)(120,186)(121,187)(122,166)
(123,167)(124,168)(125,169)(126,170)(127,171)(128,172)(129,173)(130,174)
(131,175)(132,176)(133,210)(134,211)(135,212)(136,213)(137,214)(138,215)
(139,216)(140,217)(141,218)(142,219)(143,220)(144,199)(145,200)(146,201)
(147,202)(148,203)(149,204)(150,205)(151,206)(152,207)(153,208)(154,209)
(155,188)(156,189)(157,190)(158,191)(159,192)(160,193)(161,194)(162,195)
(163,196)(164,197)(165,198);;
s3 := ( 1,111)( 2,112)( 3,113)( 4,114)( 5,115)( 6,116)( 7,117)( 8,118)
( 9,119)( 10,120)( 11,121)( 12,122)( 13,123)( 14,124)( 15,125)( 16,126)
( 17,127)( 18,128)( 19,129)( 20,130)( 21,131)( 22,132)( 23,133)( 24,134)
( 25,135)( 26,136)( 27,137)( 28,138)( 29,139)( 30,140)( 31,141)( 32,142)
( 33,143)( 34,144)( 35,145)( 36,146)( 37,147)( 38,148)( 39,149)( 40,150)
( 41,151)( 42,152)( 43,153)( 44,154)( 45,155)( 46,156)( 47,157)( 48,158)
( 49,159)( 50,160)( 51,161)( 52,162)( 53,163)( 54,164)( 55,165)( 56,166)
( 57,167)( 58,168)( 59,169)( 60,170)( 61,171)( 62,172)( 63,173)( 64,174)
( 65,175)( 66,176)( 67,177)( 68,178)( 69,179)( 70,180)( 71,181)( 72,182)
( 73,183)( 74,184)( 75,185)( 76,186)( 77,187)( 78,188)( 79,189)( 80,190)
( 81,191)( 82,192)( 83,193)( 84,194)( 85,195)( 86,196)( 87,197)( 88,198)
( 89,199)( 90,200)( 91,201)( 92,202)( 93,203)( 94,204)( 95,205)( 96,206)
( 97,207)( 98,208)( 99,209)(100,210)(101,211)(102,212)(103,213)(104,214)
(105,215)(106,216)(107,217)(108,218)(109,219)(110,220);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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(220)!( 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)(200,209)(201,208)(202,207)(203,206)(204,205)
(211,220)(212,219)(213,218)(214,217)(215,216);
s1 := Sym(220)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 46)( 13, 45)
( 14, 55)( 15, 54)( 16, 53)( 17, 52)( 18, 51)( 19, 50)( 20, 49)( 21, 48)
( 22, 47)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)
( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 56, 57)( 58, 66)( 59, 65)( 60, 64)
( 61, 63)( 67,101)( 68,100)( 69,110)( 70,109)( 71,108)( 72,107)( 73,106)
( 74,105)( 75,104)( 76,103)( 77,102)( 78, 90)( 79, 89)( 80, 99)( 81, 98)
( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)( 88, 91)(111,112)
(113,121)(114,120)(115,119)(116,118)(122,156)(123,155)(124,165)(125,164)
(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,145)
(134,144)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)
(142,147)(143,146)(166,167)(168,176)(169,175)(170,174)(171,173)(177,211)
(178,210)(179,220)(180,219)(181,218)(182,217)(183,216)(184,215)(185,214)
(186,213)(187,212)(188,200)(189,199)(190,209)(191,208)(192,207)(193,206)
(194,205)(195,204)(196,203)(197,202)(198,201);
s2 := Sym(220)!( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 16)( 6, 17)( 7, 18)
( 8, 19)( 9, 20)( 10, 21)( 11, 22)( 23, 45)( 24, 46)( 25, 47)( 26, 48)
( 27, 49)( 28, 50)( 29, 51)( 30, 52)( 31, 53)( 32, 54)( 33, 55)( 56, 67)
( 57, 68)( 58, 69)( 59, 70)( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)
( 65, 76)( 66, 77)( 78,100)( 79,101)( 80,102)( 81,103)( 82,104)( 83,105)
( 84,106)( 85,107)( 86,108)( 87,109)( 88,110)(111,177)(112,178)(113,179)
(114,180)(115,181)(116,182)(117,183)(118,184)(119,185)(120,186)(121,187)
(122,166)(123,167)(124,168)(125,169)(126,170)(127,171)(128,172)(129,173)
(130,174)(131,175)(132,176)(133,210)(134,211)(135,212)(136,213)(137,214)
(138,215)(139,216)(140,217)(141,218)(142,219)(143,220)(144,199)(145,200)
(146,201)(147,202)(148,203)(149,204)(150,205)(151,206)(152,207)(153,208)
(154,209)(155,188)(156,189)(157,190)(158,191)(159,192)(160,193)(161,194)
(162,195)(163,196)(164,197)(165,198);
s3 := Sym(220)!( 1,111)( 2,112)( 3,113)( 4,114)( 5,115)( 6,116)( 7,117)
( 8,118)( 9,119)( 10,120)( 11,121)( 12,122)( 13,123)( 14,124)( 15,125)
( 16,126)( 17,127)( 18,128)( 19,129)( 20,130)( 21,131)( 22,132)( 23,133)
( 24,134)( 25,135)( 26,136)( 27,137)( 28,138)( 29,139)( 30,140)( 31,141)
( 32,142)( 33,143)( 34,144)( 35,145)( 36,146)( 37,147)( 38,148)( 39,149)
( 40,150)( 41,151)( 42,152)( 43,153)( 44,154)( 45,155)( 46,156)( 47,157)
( 48,158)( 49,159)( 50,160)( 51,161)( 52,162)( 53,163)( 54,164)( 55,165)
( 56,166)( 57,167)( 58,168)( 59,169)( 60,170)( 61,171)( 62,172)( 63,173)
( 64,174)( 65,175)( 66,176)( 67,177)( 68,178)( 69,179)( 70,180)( 71,181)
( 72,182)( 73,183)( 74,184)( 75,185)( 76,186)( 77,187)( 78,188)( 79,189)
( 80,190)( 81,191)( 82,192)( 83,193)( 84,194)( 85,195)( 86,196)( 87,197)
( 88,198)( 89,199)( 90,200)( 91,201)( 92,202)( 93,203)( 94,204)( 95,205)
( 96,206)( 97,207)( 98,208)( 99,209)(100,210)(101,211)(102,212)(103,213)
(104,214)(105,215)(106,216)(107,217)(108,218)(109,219)(110,220);
poly := sub<Sym(220)|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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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