Polytope of Type {15,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,4,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,237638)
Rank : 4
Schlafli Type : {15,4,4}
Number of vertices, edges, etc : 15, 120, 32, 16
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   Universal
   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) :
   2-fold quotients : {15,4,4}*960a
   5-fold quotients : {3,4,4}*384a
   8-fold quotients : {15,4,2}*240
   10-fold quotients : {3,4,4}*192a
   40-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope