Polytope of Type {4,195}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,195}*1560
if this polytope has a name.
Group : SmallGroup(1560,182)
Rank : 3
Schlafli Type : {4,195}
Number of vertices, edges, etc : 4, 390, 195
Order of s₀s₁s₂ : 195
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) :
   5-fold quotients : {4,39}*312
   13-fold quotients : {4,15}*120
   65-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)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260);;
s1 := (  3,  4)(  5, 49)(  6, 50)(  7, 52)(  8, 51)(  9, 45)( 10, 46)( 11, 48)
( 12, 47)( 13, 41)( 14, 42)( 15, 44)( 16, 43)( 17, 37)( 18, 38)( 19, 40)
( 20, 39)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 25, 29)( 26, 30)( 27, 32)
( 28, 31)( 53,209)( 54,210)( 55,212)( 56,211)( 57,257)( 58,258)( 59,260)
( 60,259)( 61,253)( 62,254)( 63,256)( 64,255)( 65,249)( 66,250)( 67,252)
( 68,251)( 69,245)( 70,246)( 71,248)( 72,247)( 73,241)( 74,242)( 75,244)
( 76,243)( 77,237)( 78,238)( 79,240)( 80,239)( 81,233)( 82,234)( 83,236)
( 84,235)( 85,229)( 86,230)( 87,232)( 88,231)( 89,225)( 90,226)( 91,228)
( 92,227)( 93,221)( 94,222)( 95,224)( 96,223)( 97,217)( 98,218)( 99,220)
(100,219)(101,213)(102,214)(103,216)(104,215)(105,157)(106,158)(107,160)
(108,159)(109,205)(110,206)(111,208)(112,207)(113,201)(114,202)(115,204)
(116,203)(117,197)(118,198)(119,200)(120,199)(121,193)(122,194)(123,196)
(124,195)(125,189)(126,190)(127,192)(128,191)(129,185)(130,186)(131,188)
(132,187)(133,181)(134,182)(135,184)(136,183)(137,177)(138,178)(139,180)
(140,179)(141,173)(142,174)(143,176)(144,175)(145,169)(146,170)(147,172)
(148,171)(149,165)(150,166)(151,168)(152,167)(153,161)(154,162)(155,164)
(156,163);;
s2 := (  1, 57)(  2, 60)(  3, 59)(  4, 58)(  5, 53)(  6, 56)(  7, 55)(  8, 54)
(  9,101)( 10,104)( 11,103)( 12,102)( 13, 97)( 14,100)( 15, 99)( 16, 98)
( 17, 93)( 18, 96)( 19, 95)( 20, 94)( 21, 89)( 22, 92)( 23, 91)( 24, 90)
( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 81)( 30, 84)( 31, 83)( 32, 82)
( 33, 77)( 34, 80)( 35, 79)( 36, 78)( 37, 73)( 38, 76)( 39, 75)( 40, 74)
( 41, 69)( 42, 72)( 43, 71)( 44, 70)( 45, 65)( 46, 68)( 47, 67)( 48, 66)
( 49, 61)( 50, 64)( 51, 63)( 52, 62)(105,213)(106,216)(107,215)(108,214)
(109,209)(110,212)(111,211)(112,210)(113,257)(114,260)(115,259)(116,258)
(117,253)(118,256)(119,255)(120,254)(121,249)(122,252)(123,251)(124,250)
(125,245)(126,248)(127,247)(128,246)(129,241)(130,244)(131,243)(132,242)
(133,237)(134,240)(135,239)(136,238)(137,233)(138,236)(139,235)(140,234)
(141,229)(142,232)(143,231)(144,230)(145,225)(146,228)(147,227)(148,226)
(149,221)(150,224)(151,223)(152,222)(153,217)(154,220)(155,219)(156,218)
(157,161)(158,164)(159,163)(160,162)(165,205)(166,208)(167,207)(168,206)
(169,201)(170,204)(171,203)(172,202)(173,197)(174,200)(175,199)(176,198)
(177,193)(178,196)(179,195)(180,194)(181,189)(182,192)(183,191)(184,190)
(186,188);;
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*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(260)!(  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)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260);
s1 := Sym(260)!(  3,  4)(  5, 49)(  6, 50)(  7, 52)(  8, 51)(  9, 45)( 10, 46)
( 11, 48)( 12, 47)( 13, 41)( 14, 42)( 15, 44)( 16, 43)( 17, 37)( 18, 38)
( 19, 40)( 20, 39)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 25, 29)( 26, 30)
( 27, 32)( 28, 31)( 53,209)( 54,210)( 55,212)( 56,211)( 57,257)( 58,258)
( 59,260)( 60,259)( 61,253)( 62,254)( 63,256)( 64,255)( 65,249)( 66,250)
( 67,252)( 68,251)( 69,245)( 70,246)( 71,248)( 72,247)( 73,241)( 74,242)
( 75,244)( 76,243)( 77,237)( 78,238)( 79,240)( 80,239)( 81,233)( 82,234)
( 83,236)( 84,235)( 85,229)( 86,230)( 87,232)( 88,231)( 89,225)( 90,226)
( 91,228)( 92,227)( 93,221)( 94,222)( 95,224)( 96,223)( 97,217)( 98,218)
( 99,220)(100,219)(101,213)(102,214)(103,216)(104,215)(105,157)(106,158)
(107,160)(108,159)(109,205)(110,206)(111,208)(112,207)(113,201)(114,202)
(115,204)(116,203)(117,197)(118,198)(119,200)(120,199)(121,193)(122,194)
(123,196)(124,195)(125,189)(126,190)(127,192)(128,191)(129,185)(130,186)
(131,188)(132,187)(133,181)(134,182)(135,184)(136,183)(137,177)(138,178)
(139,180)(140,179)(141,173)(142,174)(143,176)(144,175)(145,169)(146,170)
(147,172)(148,171)(149,165)(150,166)(151,168)(152,167)(153,161)(154,162)
(155,164)(156,163);
s2 := Sym(260)!(  1, 57)(  2, 60)(  3, 59)(  4, 58)(  5, 53)(  6, 56)(  7, 55)
(  8, 54)(  9,101)( 10,104)( 11,103)( 12,102)( 13, 97)( 14,100)( 15, 99)
( 16, 98)( 17, 93)( 18, 96)( 19, 95)( 20, 94)( 21, 89)( 22, 92)( 23, 91)
( 24, 90)( 25, 85)( 26, 88)( 27, 87)( 28, 86)( 29, 81)( 30, 84)( 31, 83)
( 32, 82)( 33, 77)( 34, 80)( 35, 79)( 36, 78)( 37, 73)( 38, 76)( 39, 75)
( 40, 74)( 41, 69)( 42, 72)( 43, 71)( 44, 70)( 45, 65)( 46, 68)( 47, 67)
( 48, 66)( 49, 61)( 50, 64)( 51, 63)( 52, 62)(105,213)(106,216)(107,215)
(108,214)(109,209)(110,212)(111,211)(112,210)(113,257)(114,260)(115,259)
(116,258)(117,253)(118,256)(119,255)(120,254)(121,249)(122,252)(123,251)
(124,250)(125,245)(126,248)(127,247)(128,246)(129,241)(130,244)(131,243)
(132,242)(133,237)(134,240)(135,239)(136,238)(137,233)(138,236)(139,235)
(140,234)(141,229)(142,232)(143,231)(144,230)(145,225)(146,228)(147,227)
(148,226)(149,221)(150,224)(151,223)(152,222)(153,217)(154,220)(155,219)
(156,218)(157,161)(158,164)(159,163)(160,162)(165,205)(166,208)(167,207)
(168,206)(169,201)(170,204)(171,203)(172,202)(173,197)(174,200)(175,199)
(176,198)(177,193)(178,196)(179,195)(180,194)(181,189)(182,192)(183,191)
(184,190)(186,188);
poly := sub<Sym(260)|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*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