Polytope of Type {10,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8,4}*1280b
if this polytope has a name.
Group : SmallGroup(1280,323566)
Rank : 4
Schlafli Type : {10,8,4}
Number of vertices, edges, etc : 10, 80, 32, 8
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   2-fold quotients : {10,4,4}*640
   4-fold quotients : {10,4,4}*320
   5-fold quotients : {2,8,4}*256b
   8-fold quotients : {10,2,4}*160, {10,4,2}*160
   10-fold quotients : {2,4,4}*128
   16-fold quotients : {5,2,4}*80, {10,2,2}*80
   20-fold quotients : {2,4,4}*64
   32-fold quotients : {5,2,2}*40
   40-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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