Polytope of Type {10,40,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,40,2}*1600a
if this polytope has a name.
Group : SmallGroup(1600,8115)
Rank : 4
Schlafli Type : {10,40,2}
Number of vertices, edges, etc : 10, 200, 40, 2
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 : {10,20,2}*800a
   4-fold quotients : {10,10,2}*400a
   5-fold quotients : {2,40,2}*320, {10,8,2}*320
   10-fold quotients : {2,20,2}*160, {10,4,2}*160
   20-fold quotients : {2,10,2}*80, {10,2,2}*80
   25-fold quotients : {2,8,2}*64
   40-fold quotients : {2,5,2}*40, {5,2,2}*40
   50-fold quotients : {2,4,2}*32
   100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope