Polytope of Type {212,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {212,2}*848
if this polytope has a name.
Group : SmallGroup(848,37)
Rank : 3
Schlafli Type : {212,2}
Number of vertices, edges, etc : 212, 212, 2
Order of s0s1s2 : 212
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {212,2,2} of size 1696
Vertex Figure Of :
   {2,212,2} of size 1696
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {106,2}*424
   4-fold quotients : {53,2}*212
   53-fold quotients : {4,2}*16
   106-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {212,4}*1696, {424,2}*1696
Permutation Representation (GAP) : 
s0 := (  2, 53)(  3, 52)(  4, 51)(  5, 50)(  6, 49)(  7, 48)(  8, 47)(  9, 46)
( 10, 45)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)( 17, 38)
( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)( 23, 32)( 24, 31)( 25, 30)
( 26, 29)( 27, 28)( 55,106)( 56,105)( 57,104)( 58,103)( 59,102)( 60,101)
( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)( 67, 94)( 68, 93)
( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)( 76, 85)
( 77, 84)( 78, 83)( 79, 82)( 80, 81)(107,160)(108,212)(109,211)(110,210)
(111,209)(112,208)(113,207)(114,206)(115,205)(116,204)(117,203)(118,202)
(119,201)(120,200)(121,199)(122,198)(123,197)(124,196)(125,195)(126,194)
(127,193)(128,192)(129,191)(130,190)(131,189)(132,188)(133,187)(134,186)
(135,185)(136,184)(137,183)(138,182)(139,181)(140,180)(141,179)(142,178)
(143,177)(144,176)(145,175)(146,174)(147,173)(148,172)(149,171)(150,170)
(151,169)(152,168)(153,167)(154,166)(155,165)(156,164)(157,163)(158,162)
(159,161);;
s1 := (  1,108)(  2,107)(  3,159)(  4,158)(  5,157)(  6,156)(  7,155)(  8,154)
(  9,153)( 10,152)( 11,151)( 12,150)( 13,149)( 14,148)( 15,147)( 16,146)
( 17,145)( 18,144)( 19,143)( 20,142)( 21,141)( 22,140)( 23,139)( 24,138)
( 25,137)( 26,136)( 27,135)( 28,134)( 29,133)( 30,132)( 31,131)( 32,130)
( 33,129)( 34,128)( 35,127)( 36,126)( 37,125)( 38,124)( 39,123)( 40,122)
( 41,121)( 42,120)( 43,119)( 44,118)( 45,117)( 46,116)( 47,115)( 48,114)
( 49,113)( 50,112)( 51,111)( 52,110)( 53,109)( 54,161)( 55,160)( 56,212)
( 57,211)( 58,210)( 59,209)( 60,208)( 61,207)( 62,206)( 63,205)( 64,204)
( 65,203)( 66,202)( 67,201)( 68,200)( 69,199)( 70,198)( 71,197)( 72,196)
( 73,195)( 74,194)( 75,193)( 76,192)( 77,191)( 78,190)( 79,189)( 80,188)
( 81,187)( 82,186)( 83,185)( 84,184)( 85,183)( 86,182)( 87,181)( 88,180)
( 89,179)( 90,178)( 91,177)( 92,176)( 93,175)( 94,174)( 95,173)( 96,172)
( 97,171)( 98,170)( 99,169)(100,168)(101,167)(102,166)(103,165)(104,164)
(105,163)(106,162);;
s2 := (213,214);;
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, 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*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*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(214)!(  2, 53)(  3, 52)(  4, 51)(  5, 50)(  6, 49)(  7, 48)(  8, 47)
(  9, 46)( 10, 45)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)
( 17, 38)( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)( 23, 32)( 24, 31)
( 25, 30)( 26, 29)( 27, 28)( 55,106)( 56,105)( 57,104)( 58,103)( 59,102)
( 60,101)( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)( 67, 94)
( 68, 93)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)
( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 80, 81)(107,160)(108,212)(109,211)
(110,210)(111,209)(112,208)(113,207)(114,206)(115,205)(116,204)(117,203)
(118,202)(119,201)(120,200)(121,199)(122,198)(123,197)(124,196)(125,195)
(126,194)(127,193)(128,192)(129,191)(130,190)(131,189)(132,188)(133,187)
(134,186)(135,185)(136,184)(137,183)(138,182)(139,181)(140,180)(141,179)
(142,178)(143,177)(144,176)(145,175)(146,174)(147,173)(148,172)(149,171)
(150,170)(151,169)(152,168)(153,167)(154,166)(155,165)(156,164)(157,163)
(158,162)(159,161);
s1 := Sym(214)!(  1,108)(  2,107)(  3,159)(  4,158)(  5,157)(  6,156)(  7,155)
(  8,154)(  9,153)( 10,152)( 11,151)( 12,150)( 13,149)( 14,148)( 15,147)
( 16,146)( 17,145)( 18,144)( 19,143)( 20,142)( 21,141)( 22,140)( 23,139)
( 24,138)( 25,137)( 26,136)( 27,135)( 28,134)( 29,133)( 30,132)( 31,131)
( 32,130)( 33,129)( 34,128)( 35,127)( 36,126)( 37,125)( 38,124)( 39,123)
( 40,122)( 41,121)( 42,120)( 43,119)( 44,118)( 45,117)( 46,116)( 47,115)
( 48,114)( 49,113)( 50,112)( 51,111)( 52,110)( 53,109)( 54,161)( 55,160)
( 56,212)( 57,211)( 58,210)( 59,209)( 60,208)( 61,207)( 62,206)( 63,205)
( 64,204)( 65,203)( 66,202)( 67,201)( 68,200)( 69,199)( 70,198)( 71,197)
( 72,196)( 73,195)( 74,194)( 75,193)( 76,192)( 77,191)( 78,190)( 79,189)
( 80,188)( 81,187)( 82,186)( 83,185)( 84,184)( 85,183)( 86,182)( 87,181)
( 88,180)( 89,179)( 90,178)( 91,177)( 92,176)( 93,175)( 94,174)( 95,173)
( 96,172)( 97,171)( 98,170)( 99,169)(100,168)(101,167)(102,166)(103,165)
(104,164)(105,163)(106,162);
s2 := Sym(214)!(213,214);
poly := sub<Sym(214)|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, 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*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*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 >;

to this polytope