Polytope of Type {48,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,4,2}*768a
if this polytope has a name.
Group : SmallGroup(768,323306)
Rank : 4
Schlafli Type : {48,4,2}
Number of vertices, edges, etc : 48, 96, 4, 2
Order of s₀s₁s₂s₃ : 48
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 : {24,4,2}*384a, {48,2,2}*384
   3-fold quotients : {16,4,2}*256a
   4-fold quotients : {12,4,2}*192a, {24,2,2}*192
   6-fold quotients : {8,4,2}*128a, {16,2,2}*128
   8-fold quotients : {12,2,2}*96, {6,4,2}*96a
   12-fold quotients : {4,4,2}*64, {8,2,2}*64
   16-fold quotients : {6,2,2}*48
   24-fold quotients : {2,4,2}*32, {4,2,2}*32
   32-fold quotients : {3,2,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope