Polytope of Type {183,4}

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

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