Polytope of Type {2,10,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,40}*1600c
if this polytope has a name.
Group : SmallGroup(1600,8648)
Rank : 4
Schlafli Type : {2,10,40}
Number of vertices, edges, etc : 2, 10, 200, 40
Order of s₀s₁s₂s₃ : 40
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) :
   2-fold quotients : {2,10,20}*800c
   4-fold quotients : {2,10,10}*400c
   5-fold quotients : {2,10,8}*320
   8-fold quotients : {2,5,10}*200
   10-fold quotients : {2,10,4}*160
   20-fold quotients : {2,10,2}*80
   25-fold quotients : {2,2,8}*64
   40-fold quotients : {2,5,2}*40
   50-fold quotients : {2,2,4}*32
   100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  8, 23)(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 18)
( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 29, 32)( 30, 31)( 33, 48)( 34, 52)
( 35, 51)( 36, 50)( 37, 49)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)
( 54, 57)( 55, 56)( 58, 73)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 68)
( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 79, 82)( 80, 81)( 83, 98)( 84,102)
( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)( 91, 95)( 92, 94)
(104,107)(105,106)(108,123)(109,127)(110,126)(111,125)(112,124)(113,118)
(114,122)(115,121)(116,120)(117,119)(129,132)(130,131)(133,148)(134,152)
(135,151)(136,150)(137,149)(138,143)(139,147)(140,146)(141,145)(142,144)
(154,157)(155,156)(158,173)(159,177)(160,176)(161,175)(162,174)(163,168)
(164,172)(165,171)(166,170)(167,169)(179,182)(180,181)(183,198)(184,202)
(185,201)(186,200)(187,199)(188,193)(189,197)(190,196)(191,195)(192,194);;
s2 := (  3,109)(  4,108)(  5,112)(  6,111)(  7,110)(  8,104)(  9,103)( 10,107)
( 11,106)( 12,105)( 13,124)( 14,123)( 15,127)( 16,126)( 17,125)( 18,119)
( 19,118)( 20,122)( 21,121)( 22,120)( 23,114)( 24,113)( 25,117)( 26,116)
( 27,115)( 28,134)( 29,133)( 30,137)( 31,136)( 32,135)( 33,129)( 34,128)
( 35,132)( 36,131)( 37,130)( 38,149)( 39,148)( 40,152)( 41,151)( 42,150)
( 43,144)( 44,143)( 45,147)( 46,146)( 47,145)( 48,139)( 49,138)( 50,142)
( 51,141)( 52,140)( 53,184)( 54,183)( 55,187)( 56,186)( 57,185)( 58,179)
( 59,178)( 60,182)( 61,181)( 62,180)( 63,199)( 64,198)( 65,202)( 66,201)
( 67,200)( 68,194)( 69,193)( 70,197)( 71,196)( 72,195)( 73,189)( 74,188)
( 75,192)( 76,191)( 77,190)( 78,159)( 79,158)( 80,162)( 81,161)( 82,160)
( 83,154)( 84,153)( 85,157)( 86,156)( 87,155)( 88,174)( 89,173)( 90,177)
( 91,176)( 92,175)( 93,169)( 94,168)( 95,172)( 96,171)( 97,170)( 98,164)
( 99,163)(100,167)(101,166)(102,165);;
s3 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 53, 78)( 54, 82)( 55, 81)( 56, 80)
( 57, 79)( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)( 64, 92)
( 65, 91)( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)( 72, 94)
( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99)(103,153)(104,157)(105,156)
(106,155)(107,154)(108,158)(109,162)(110,161)(111,160)(112,159)(113,163)
(114,167)(115,166)(116,165)(117,164)(118,168)(119,172)(120,171)(121,170)
(122,169)(123,173)(124,177)(125,176)(126,175)(127,174)(128,178)(129,182)
(130,181)(131,180)(132,179)(133,183)(134,187)(135,186)(136,185)(137,184)
(138,188)(139,192)(140,191)(141,190)(142,189)(143,193)(144,197)(145,196)
(146,195)(147,194)(148,198)(149,202)(150,201)(151,200)(152,199);;
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, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*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(202)!(1,2);
s1 := Sym(202)!(  4,  7)(  5,  6)(  8, 23)(  9, 27)( 10, 26)( 11, 25)( 12, 24)
( 13, 18)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 29, 32)( 30, 31)( 33, 48)
( 34, 52)( 35, 51)( 36, 50)( 37, 49)( 38, 43)( 39, 47)( 40, 46)( 41, 45)
( 42, 44)( 54, 57)( 55, 56)( 58, 73)( 59, 77)( 60, 76)( 61, 75)( 62, 74)
( 63, 68)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 79, 82)( 80, 81)( 83, 98)
( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)( 91, 95)
( 92, 94)(104,107)(105,106)(108,123)(109,127)(110,126)(111,125)(112,124)
(113,118)(114,122)(115,121)(116,120)(117,119)(129,132)(130,131)(133,148)
(134,152)(135,151)(136,150)(137,149)(138,143)(139,147)(140,146)(141,145)
(142,144)(154,157)(155,156)(158,173)(159,177)(160,176)(161,175)(162,174)
(163,168)(164,172)(165,171)(166,170)(167,169)(179,182)(180,181)(183,198)
(184,202)(185,201)(186,200)(187,199)(188,193)(189,197)(190,196)(191,195)
(192,194);
s2 := Sym(202)!(  3,109)(  4,108)(  5,112)(  6,111)(  7,110)(  8,104)(  9,103)
( 10,107)( 11,106)( 12,105)( 13,124)( 14,123)( 15,127)( 16,126)( 17,125)
( 18,119)( 19,118)( 20,122)( 21,121)( 22,120)( 23,114)( 24,113)( 25,117)
( 26,116)( 27,115)( 28,134)( 29,133)( 30,137)( 31,136)( 32,135)( 33,129)
( 34,128)( 35,132)( 36,131)( 37,130)( 38,149)( 39,148)( 40,152)( 41,151)
( 42,150)( 43,144)( 44,143)( 45,147)( 46,146)( 47,145)( 48,139)( 49,138)
( 50,142)( 51,141)( 52,140)( 53,184)( 54,183)( 55,187)( 56,186)( 57,185)
( 58,179)( 59,178)( 60,182)( 61,181)( 62,180)( 63,199)( 64,198)( 65,202)
( 66,201)( 67,200)( 68,194)( 69,193)( 70,197)( 71,196)( 72,195)( 73,189)
( 74,188)( 75,192)( 76,191)( 77,190)( 78,159)( 79,158)( 80,162)( 81,161)
( 82,160)( 83,154)( 84,153)( 85,157)( 86,156)( 87,155)( 88,174)( 89,173)
( 90,177)( 91,176)( 92,175)( 93,169)( 94,168)( 95,172)( 96,171)( 97,170)
( 98,164)( 99,163)(100,167)(101,166)(102,165);
s3 := Sym(202)!(  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 53, 78)( 54, 82)( 55, 81)
( 56, 80)( 57, 79)( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)
( 64, 92)( 65, 91)( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)
( 72, 94)( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99)(103,153)(104,157)
(105,156)(106,155)(107,154)(108,158)(109,162)(110,161)(111,160)(112,159)
(113,163)(114,167)(115,166)(116,165)(117,164)(118,168)(119,172)(120,171)
(121,170)(122,169)(123,173)(124,177)(125,176)(126,175)(127,174)(128,178)
(129,182)(130,181)(131,180)(132,179)(133,183)(134,187)(135,186)(136,185)
(137,184)(138,188)(139,192)(140,191)(141,190)(142,189)(143,193)(144,197)
(145,196)(146,195)(147,194)(148,198)(149,202)(150,201)(151,200)(152,199);
poly := sub<Sym(202)|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, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope