Polytope of Type {74,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {74,6}*888
Also Known As : {74,6|2}. if this polytope has another name.
Group : SmallGroup(888,54)
Rank : 3
Schlafli Type : {74,6}
Number of vertices, edges, etc : 74, 222, 6
Order of s0s1s2 : 222
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {74,6,2} of size 1776
Vertex Figure Of :
   {2,74,6} of size 1776
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {74,2}*296
   6-fold quotients : {37,2}*148
   37-fold quotients : {2,6}*24
   74-fold quotients : {2,3}*12
   111-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {74,12}*1776, {148,6}*1776a
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) : 
s0 := (  2, 37)(  3, 36)(  4, 35)(  5, 34)(  6, 33)(  7, 32)(  8, 31)(  9, 30)( 10, 29)( 11, 28)( 12, 27)( 13, 26)( 14, 25)( 15, 24)( 16, 23)( 17, 22)( 18, 21)( 19, 20)( 39, 74)( 40, 73)( 41, 72)( 42, 71)( 43, 70)( 44, 69)( 45, 68)( 46, 67)( 47, 66)( 48, 65)( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 76,111)( 77,110)( 78,109)( 79,108)( 80,107)( 81,106)( 82,105)( 83,104)( 84,103)( 85,102)( 86,101)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 91, 96)( 92, 95)( 93, 94)(113,148)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,141)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131)(150,185)(151,184)(152,183)(153,182)(154,181)(155,180)(156,179)(157,178)(158,177)(159,176)(160,175)(161,174)(162,173)(163,172)(164,171)(165,170)(166,169)(167,168)(187,222)(188,221)(189,220)(190,219)(191,218)(192,217)(193,216)(194,215)(195,214)(196,213)(197,212)(198,211)(199,210)(200,209)(201,208)(202,207)(203,206)(204,205);;
s1 := (  1,  2)(  3, 37)(  4, 36)(  5, 35)(  6, 34)(  7, 33)(  8, 32)(  9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 38, 76)( 39, 75)( 40,111)( 41,110)( 42,109)( 43,108)( 44,107)( 45,106)( 46,105)( 47,104)( 48,103)( 49,102)( 50,101)( 51,100)( 52, 99)( 53, 98)( 54, 97)( 55, 96)( 56, 95)( 57, 94)( 58, 93)( 59, 92)( 60, 91)( 61, 90)( 62, 89)( 63, 88)( 64, 87)( 65, 86)( 66, 85)( 67, 84)( 68, 83)( 69, 82)( 70, 81)( 71, 80)( 72, 79)( 73, 78)( 74, 77)(112,113)(114,148)(115,147)(116,146)(117,145)(118,144)(119,143)(120,142)(121,141)(122,140)(123,139)(124,138)(125,137)(126,136)(127,135)(128,134)(129,133)(130,132)(149,187)(150,186)(151,222)(152,221)(153,220)(154,219)(155,218)(156,217)(157,216)(158,215)(159,214)(160,213)(161,212)(162,211)(163,210)(164,209)(165,208)(166,207)(167,206)(168,205)(169,204)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)(176,197)(177,196)(178,195)(179,194)(180,193)(181,192)(182,191)(183,190)(184,189)(185,188);;
s2 := (  1,149)(  2,150)(  3,151)(  4,152)(  5,153)(  6,154)(  7,155)(  8,156)(  9,157)( 10,158)( 11,159)( 12,160)( 13,161)( 14,162)( 15,163)( 16,164)( 17,165)( 18,166)( 19,167)( 20,168)( 21,169)( 22,170)( 23,171)( 24,172)( 25,173)( 26,174)( 27,175)( 28,176)( 29,177)( 30,178)( 31,179)( 32,180)( 33,181)( 34,182)( 35,183)( 36,184)( 37,185)( 38,112)( 39,113)( 40,114)( 41,115)( 42,116)( 43,117)( 44,118)( 45,119)( 46,120)( 47,121)( 48,122)( 49,123)( 50,124)( 51,125)( 52,126)( 53,127)( 54,128)( 55,129)( 56,130)( 57,131)( 58,132)( 59,133)( 60,134)( 61,135)( 62,136)( 63,137)( 64,138)( 65,139)( 66,140)( 67,141)( 68,142)( 69,143)( 70,144)( 71,145)( 72,146)( 73,147)( 74,148)( 75,186)( 76,187)( 77,188)( 78,189)( 79,190)( 80,191)( 81,192)( 82,193)( 83,194)( 84,195)( 85,196)( 86,197)( 87,198)( 88,199)( 89,200)( 90,201)( 91,202)( 92,203)( 93,204)( 94,205)( 95,206)( 96,207)( 97,208)( 98,209)( 99,210)(100,211)(101,212)(102,213)(103,214)(104,215)(105,216)(106,217)(107,218)(108,219)(109,220)(110,221)(111,222);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(222)!(  2, 37)(  3, 36)(  4, 35)(  5, 34)(  6, 33)(  7, 32)(  8, 31)(  9, 30)( 10, 29)( 11, 28)( 12, 27)( 13, 26)( 14, 25)( 15, 24)( 16, 23)( 17, 22)( 18, 21)( 19, 20)( 39, 74)( 40, 73)( 41, 72)( 42, 71)( 43, 70)( 44, 69)( 45, 68)( 46, 67)( 47, 66)( 48, 65)( 49, 64)( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58)( 56, 57)( 76,111)( 77,110)( 78,109)( 79,108)( 80,107)( 81,106)( 82,105)( 83,104)( 84,103)( 85,102)( 86,101)( 87,100)( 88, 99)( 89, 98)( 90, 97)( 91, 96)( 92, 95)( 93, 94)(113,148)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,141)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131)(150,185)(151,184)(152,183)(153,182)(154,181)(155,180)(156,179)(157,178)(158,177)(159,176)(160,175)(161,174)(162,173)(163,172)(164,171)(165,170)(166,169)(167,168)(187,222)(188,221)(189,220)(190,219)(191,218)(192,217)(193,216)(194,215)(195,214)(196,213)(197,212)(198,211)(199,210)(200,209)(201,208)(202,207)(203,206)(204,205);
s1 := Sym(222)!(  1,  2)(  3, 37)(  4, 36)(  5, 35)(  6, 34)(  7, 33)(  8, 32)(  9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 38, 76)( 39, 75)( 40,111)( 41,110)( 42,109)( 43,108)( 44,107)( 45,106)( 46,105)( 47,104)( 48,103)( 49,102)( 50,101)( 51,100)( 52, 99)( 53, 98)( 54, 97)( 55, 96)( 56, 95)( 57, 94)( 58, 93)( 59, 92)( 60, 91)( 61, 90)( 62, 89)( 63, 88)( 64, 87)( 65, 86)( 66, 85)( 67, 84)( 68, 83)( 69, 82)( 70, 81)( 71, 80)( 72, 79)( 73, 78)( 74, 77)(112,113)(114,148)(115,147)(116,146)(117,145)(118,144)(119,143)(120,142)(121,141)(122,140)(123,139)(124,138)(125,137)(126,136)(127,135)(128,134)(129,133)(130,132)(149,187)(150,186)(151,222)(152,221)(153,220)(154,219)(155,218)(156,217)(157,216)(158,215)(159,214)(160,213)(161,212)(162,211)(163,210)(164,209)(165,208)(166,207)(167,206)(168,205)(169,204)(170,203)(171,202)(172,201)(173,200)(174,199)(175,198)(176,197)(177,196)(178,195)(179,194)(180,193)(181,192)(182,191)(183,190)(184,189)(185,188);
s2 := Sym(222)!(  1,149)(  2,150)(  3,151)(  4,152)(  5,153)(  6,154)(  7,155)(  8,156)(  9,157)( 10,158)( 11,159)( 12,160)( 13,161)( 14,162)( 15,163)( 16,164)( 17,165)( 18,166)( 19,167)( 20,168)( 21,169)( 22,170)( 23,171)( 24,172)( 25,173)( 26,174)( 27,175)( 28,176)( 29,177)( 30,178)( 31,179)( 32,180)( 33,181)( 34,182)( 35,183)( 36,184)( 37,185)( 38,112)( 39,113)( 40,114)( 41,115)( 42,116)( 43,117)( 44,118)( 45,119)( 46,120)( 47,121)( 48,122)( 49,123)( 50,124)( 51,125)( 52,126)( 53,127)( 54,128)( 55,129)( 56,130)( 57,131)( 58,132)( 59,133)( 60,134)( 61,135)( 62,136)( 63,137)( 64,138)( 65,139)( 66,140)( 67,141)( 68,142)( 69,143)( 70,144)( 71,145)( 72,146)( 73,147)( 74,148)( 75,186)( 76,187)( 77,188)( 78,189)( 79,190)( 80,191)( 81,192)( 82,193)( 83,194)( 84,195)( 85,196)( 86,197)( 87,198)( 88,199)( 89,200)( 90,201)( 91,202)( 92,203)( 93,204)( 94,205)( 95,206)( 96,207)( 97,208)( 98,209)( 99,210)(100,211)(101,212)(102,213)(103,214)(104,215)(105,216)(106,217)(107,218)(108,219)(109,220)(110,221)(111,222);
poly := sub<Sym(222)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
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*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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle