Polytope of Type {2,10,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,38}*1520
if this polytope has a name.
Group : SmallGroup(1520,174)
Rank : 4
Schlafli Type : {2,10,38}
Number of vertices, edges, etc : 2, 10, 190, 38
Order of s₀s₁s₂s₃ : 190
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,2,38}*304
   10-fold quotients : {2,2,19}*152
   19-fold quotients : {2,10,2}*80
   38-fold quotients : {2,5,2}*40
   95-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 22, 79)( 23, 80)( 24, 81)( 25, 82)( 26, 83)( 27, 84)( 28, 85)( 29, 86)
( 30, 87)( 31, 88)( 32, 89)( 33, 90)( 34, 91)( 35, 92)( 36, 93)( 37, 94)
( 38, 95)( 39, 96)( 40, 97)( 41, 60)( 42, 61)( 43, 62)( 44, 63)( 45, 64)
( 46, 65)( 47, 66)( 48, 67)( 49, 68)( 50, 69)( 51, 70)( 52, 71)( 53, 72)
( 54, 73)( 55, 74)( 56, 75)( 57, 76)( 58, 77)( 59, 78)(117,174)(118,175)
(119,176)(120,177)(121,178)(122,179)(123,180)(124,181)(125,182)(126,183)
(127,184)(128,185)(129,186)(130,187)(131,188)(132,189)(133,190)(134,191)
(135,192)(136,155)(137,156)(138,157)(139,158)(140,159)(141,160)(142,161)
(143,162)(144,163)(145,164)(146,165)(147,166)(148,167)(149,168)(150,169)
(151,170)(152,171)(153,172)(154,173);;
s2 := (  3, 22)(  4, 40)(  5, 39)(  6, 38)(  7, 37)(  8, 36)(  9, 35)( 10, 34)
( 11, 33)( 12, 32)( 13, 31)( 14, 30)( 15, 29)( 16, 28)( 17, 27)( 18, 26)
( 19, 25)( 20, 24)( 21, 23)( 41, 79)( 42, 97)( 43, 96)( 44, 95)( 45, 94)
( 46, 93)( 47, 92)( 48, 91)( 49, 90)( 50, 89)( 51, 88)( 52, 87)( 53, 86)
( 54, 85)( 55, 84)( 56, 83)( 57, 82)( 58, 81)( 59, 80)( 61, 78)( 62, 77)
( 63, 76)( 64, 75)( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 69, 70)( 98,117)
( 99,135)(100,134)(101,133)(102,132)(103,131)(104,130)(105,129)(106,128)
(107,127)(108,126)(109,125)(110,124)(111,123)(112,122)(113,121)(114,120)
(115,119)(116,118)(136,174)(137,192)(138,191)(139,190)(140,189)(141,188)
(142,187)(143,186)(144,185)(145,184)(146,183)(147,182)(148,181)(149,180)
(150,179)(151,178)(152,177)(153,176)(154,175)(156,173)(157,172)(158,171)
(159,170)(160,169)(161,168)(162,167)(163,166)(164,165);;
s3 := (  3, 99)(  4, 98)(  5,116)(  6,115)(  7,114)(  8,113)(  9,112)( 10,111)
( 11,110)( 12,109)( 13,108)( 14,107)( 15,106)( 16,105)( 17,104)( 18,103)
( 19,102)( 20,101)( 21,100)( 22,118)( 23,117)( 24,135)( 25,134)( 26,133)
( 27,132)( 28,131)( 29,130)( 30,129)( 31,128)( 32,127)( 33,126)( 34,125)
( 35,124)( 36,123)( 37,122)( 38,121)( 39,120)( 40,119)( 41,137)( 42,136)
( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)( 48,149)( 49,148)( 50,147)
( 51,146)( 52,145)( 53,144)( 54,143)( 55,142)( 56,141)( 57,140)( 58,139)
( 59,138)( 60,156)( 61,155)( 62,173)( 63,172)( 64,171)( 65,170)( 66,169)
( 67,168)( 68,167)( 69,166)( 70,165)( 71,164)( 72,163)( 73,162)( 74,161)
( 75,160)( 76,159)( 77,158)( 78,157)( 79,175)( 80,174)( 81,192)( 82,191)
( 83,190)( 84,189)( 85,188)( 86,187)( 87,186)( 88,185)( 89,184)( 90,183)
( 91,182)( 92,181)( 93,180)( 94,179)( 95,178)( 96,177)( 97,176);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(192)!(1,2);
s1 := Sym(192)!( 22, 79)( 23, 80)( 24, 81)( 25, 82)( 26, 83)( 27, 84)( 28, 85)
( 29, 86)( 30, 87)( 31, 88)( 32, 89)( 33, 90)( 34, 91)( 35, 92)( 36, 93)
( 37, 94)( 38, 95)( 39, 96)( 40, 97)( 41, 60)( 42, 61)( 43, 62)( 44, 63)
( 45, 64)( 46, 65)( 47, 66)( 48, 67)( 49, 68)( 50, 69)( 51, 70)( 52, 71)
( 53, 72)( 54, 73)( 55, 74)( 56, 75)( 57, 76)( 58, 77)( 59, 78)(117,174)
(118,175)(119,176)(120,177)(121,178)(122,179)(123,180)(124,181)(125,182)
(126,183)(127,184)(128,185)(129,186)(130,187)(131,188)(132,189)(133,190)
(134,191)(135,192)(136,155)(137,156)(138,157)(139,158)(140,159)(141,160)
(142,161)(143,162)(144,163)(145,164)(146,165)(147,166)(148,167)(149,168)
(150,169)(151,170)(152,171)(153,172)(154,173);
s2 := Sym(192)!(  3, 22)(  4, 40)(  5, 39)(  6, 38)(  7, 37)(  8, 36)(  9, 35)
( 10, 34)( 11, 33)( 12, 32)( 13, 31)( 14, 30)( 15, 29)( 16, 28)( 17, 27)
( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 41, 79)( 42, 97)( 43, 96)( 44, 95)
( 45, 94)( 46, 93)( 47, 92)( 48, 91)( 49, 90)( 50, 89)( 51, 88)( 52, 87)
( 53, 86)( 54, 85)( 55, 84)( 56, 83)( 57, 82)( 58, 81)( 59, 80)( 61, 78)
( 62, 77)( 63, 76)( 64, 75)( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 69, 70)
( 98,117)( 99,135)(100,134)(101,133)(102,132)(103,131)(104,130)(105,129)
(106,128)(107,127)(108,126)(109,125)(110,124)(111,123)(112,122)(113,121)
(114,120)(115,119)(116,118)(136,174)(137,192)(138,191)(139,190)(140,189)
(141,188)(142,187)(143,186)(144,185)(145,184)(146,183)(147,182)(148,181)
(149,180)(150,179)(151,178)(152,177)(153,176)(154,175)(156,173)(157,172)
(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)(164,165);
s3 := Sym(192)!(  3, 99)(  4, 98)(  5,116)(  6,115)(  7,114)(  8,113)(  9,112)
( 10,111)( 11,110)( 12,109)( 13,108)( 14,107)( 15,106)( 16,105)( 17,104)
( 18,103)( 19,102)( 20,101)( 21,100)( 22,118)( 23,117)( 24,135)( 25,134)
( 26,133)( 27,132)( 28,131)( 29,130)( 30,129)( 31,128)( 32,127)( 33,126)
( 34,125)( 35,124)( 36,123)( 37,122)( 38,121)( 39,120)( 40,119)( 41,137)
( 42,136)( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)( 48,149)( 49,148)
( 50,147)( 51,146)( 52,145)( 53,144)( 54,143)( 55,142)( 56,141)( 57,140)
( 58,139)( 59,138)( 60,156)( 61,155)( 62,173)( 63,172)( 64,171)( 65,170)
( 66,169)( 67,168)( 68,167)( 69,166)( 70,165)( 71,164)( 72,163)( 73,162)
( 74,161)( 75,160)( 76,159)( 77,158)( 78,157)( 79,175)( 80,174)( 81,192)
( 82,191)( 83,190)( 84,189)( 85,188)( 86,187)( 87,186)( 88,185)( 89,184)
( 90,183)( 91,182)( 92,181)( 93,180)( 94,179)( 95,178)( 96,177)( 97,176);
poly := sub<Sym(192)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope