Polytope of Type {4,183}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,183}*1464
if this polytope has a name.
Group : SmallGroup(1464,48)
Rank : 3
Schlafli Type : {4,183}
Number of vertices, edges, etc : 4, 366, 183
Order of s₀s₁s₂ : 183
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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) :
   61-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244);;
s1 := (  3,  4)(  5,241)(  6,242)(  7,244)(  8,243)(  9,237)( 10,238)( 11,240)
( 12,239)( 13,233)( 14,234)( 15,236)( 16,235)( 17,229)( 18,230)( 19,232)
( 20,231)( 21,225)( 22,226)( 23,228)( 24,227)( 25,221)( 26,222)( 27,224)
( 28,223)( 29,217)( 30,218)( 31,220)( 32,219)( 33,213)( 34,214)( 35,216)
( 36,215)( 37,209)( 38,210)( 39,212)( 40,211)( 41,205)( 42,206)( 43,208)
( 44,207)( 45,201)( 46,202)( 47,204)( 48,203)( 49,197)( 50,198)( 51,200)
( 52,199)( 53,193)( 54,194)( 55,196)( 56,195)( 57,189)( 58,190)( 59,192)
( 60,191)( 61,185)( 62,186)( 63,188)( 64,187)( 65,181)( 66,182)( 67,184)
( 68,183)( 69,177)( 70,178)( 71,180)( 72,179)( 73,173)( 74,174)( 75,176)
( 76,175)( 77,169)( 78,170)( 79,172)( 80,171)( 81,165)( 82,166)( 83,168)
( 84,167)( 85,161)( 86,162)( 87,164)( 88,163)( 89,157)( 90,158)( 91,160)
( 92,159)( 93,153)( 94,154)( 95,156)( 96,155)( 97,149)( 98,150)( 99,152)
(100,151)(101,145)(102,146)(103,148)(104,147)(105,141)(106,142)(107,144)
(108,143)(109,137)(110,138)(111,140)(112,139)(113,133)(114,134)(115,136)
(116,135)(117,129)(118,130)(119,132)(120,131)(121,125)(122,126)(123,128)
(124,127);;
s2 := (  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,241)( 10,244)( 11,243)( 12,242)
( 13,237)( 14,240)( 15,239)( 16,238)( 17,233)( 18,236)( 19,235)( 20,234)
( 21,229)( 22,232)( 23,231)( 24,230)( 25,225)( 26,228)( 27,227)( 28,226)
( 29,221)( 30,224)( 31,223)( 32,222)( 33,217)( 34,220)( 35,219)( 36,218)
( 37,213)( 38,216)( 39,215)( 40,214)( 41,209)( 42,212)( 43,211)( 44,210)
( 45,205)( 46,208)( 47,207)( 48,206)( 49,201)( 50,204)( 51,203)( 52,202)
( 53,197)( 54,200)( 55,199)( 56,198)( 57,193)( 58,196)( 59,195)( 60,194)
( 61,189)( 62,192)( 63,191)( 64,190)( 65,185)( 66,188)( 67,187)( 68,186)
( 69,181)( 70,184)( 71,183)( 72,182)( 73,177)( 74,180)( 75,179)( 76,178)
( 77,173)( 78,176)( 79,175)( 80,174)( 81,169)( 82,172)( 83,171)( 84,170)
( 85,165)( 86,168)( 87,167)( 88,166)( 89,161)( 90,164)( 91,163)( 92,162)
( 93,157)( 94,160)( 95,159)( 96,158)( 97,153)( 98,156)( 99,155)(100,154)
(101,149)(102,152)(103,151)(104,150)(105,145)(106,148)(107,147)(108,146)
(109,141)(110,144)(111,143)(112,142)(113,137)(114,140)(115,139)(116,138)
(117,133)(118,136)(119,135)(120,134)(121,129)(122,132)(123,131)(124,130)
(126,128);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(244)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244);
s1 := Sym(244)!(  3,  4)(  5,241)(  6,242)(  7,244)(  8,243)(  9,237)( 10,238)
( 11,240)( 12,239)( 13,233)( 14,234)( 15,236)( 16,235)( 17,229)( 18,230)
( 19,232)( 20,231)( 21,225)( 22,226)( 23,228)( 24,227)( 25,221)( 26,222)
( 27,224)( 28,223)( 29,217)( 30,218)( 31,220)( 32,219)( 33,213)( 34,214)
( 35,216)( 36,215)( 37,209)( 38,210)( 39,212)( 40,211)( 41,205)( 42,206)
( 43,208)( 44,207)( 45,201)( 46,202)( 47,204)( 48,203)( 49,197)( 50,198)
( 51,200)( 52,199)( 53,193)( 54,194)( 55,196)( 56,195)( 57,189)( 58,190)
( 59,192)( 60,191)( 61,185)( 62,186)( 63,188)( 64,187)( 65,181)( 66,182)
( 67,184)( 68,183)( 69,177)( 70,178)( 71,180)( 72,179)( 73,173)( 74,174)
( 75,176)( 76,175)( 77,169)( 78,170)( 79,172)( 80,171)( 81,165)( 82,166)
( 83,168)( 84,167)( 85,161)( 86,162)( 87,164)( 88,163)( 89,157)( 90,158)
( 91,160)( 92,159)( 93,153)( 94,154)( 95,156)( 96,155)( 97,149)( 98,150)
( 99,152)(100,151)(101,145)(102,146)(103,148)(104,147)(105,141)(106,142)
(107,144)(108,143)(109,137)(110,138)(111,140)(112,139)(113,133)(114,134)
(115,136)(116,135)(117,129)(118,130)(119,132)(120,131)(121,125)(122,126)
(123,128)(124,127);
s2 := Sym(244)!(  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,241)( 10,244)( 11,243)
( 12,242)( 13,237)( 14,240)( 15,239)( 16,238)( 17,233)( 18,236)( 19,235)
( 20,234)( 21,229)( 22,232)( 23,231)( 24,230)( 25,225)( 26,228)( 27,227)
( 28,226)( 29,221)( 30,224)( 31,223)( 32,222)( 33,217)( 34,220)( 35,219)
( 36,218)( 37,213)( 38,216)( 39,215)( 40,214)( 41,209)( 42,212)( 43,211)
( 44,210)( 45,205)( 46,208)( 47,207)( 48,206)( 49,201)( 50,204)( 51,203)
( 52,202)( 53,197)( 54,200)( 55,199)( 56,198)( 57,193)( 58,196)( 59,195)
( 60,194)( 61,189)( 62,192)( 63,191)( 64,190)( 65,185)( 66,188)( 67,187)
( 68,186)( 69,181)( 70,184)( 71,183)( 72,182)( 73,177)( 74,180)( 75,179)
( 76,178)( 77,173)( 78,176)( 79,175)( 80,174)( 81,169)( 82,172)( 83,171)
( 84,170)( 85,165)( 86,168)( 87,167)( 88,166)( 89,161)( 90,164)( 91,163)
( 92,162)( 93,157)( 94,160)( 95,159)( 96,158)( 97,153)( 98,156)( 99,155)
(100,154)(101,149)(102,152)(103,151)(104,150)(105,145)(106,148)(107,147)
(108,146)(109,141)(110,144)(111,143)(112,142)(113,137)(114,140)(115,139)
(116,138)(117,133)(118,136)(119,135)(120,134)(121,129)(122,132)(123,131)
(124,130)(126,128);
poly := sub<Sym(244)|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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope