Polytope of Type {24,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8,2}*768c
if this polytope has a name.
Group : SmallGroup(768,145174)
Rank : 4
Schlafli Type : {24,8,2}
Number of vertices, edges, etc : 24, 96, 8, 2
Order of s₀s₁s₂s₃ : 24
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, {12,8,2}*384a
   3-fold quotients : {8,8,2}*256b
   4-fold quotients : {12,4,2}*192a, {24,2,2}*192, {6,8,2}*192
   6-fold quotients : {4,8,2}*128a, {8,4,2}*128a
   8-fold quotients : {12,2,2}*96, {6,4,2}*96a
   12-fold quotients : {4,4,2}*64, {2,8,2}*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 := (  1,145)(  2,147)(  3,146)(  4,148)(  5,150)(  6,149)(  7,151)(  8,153)
(  9,152)( 10,154)( 11,156)( 12,155)( 13,157)( 14,159)( 15,158)( 16,160)
( 17,162)( 18,161)( 19,163)( 20,165)( 21,164)( 22,166)( 23,168)( 24,167)
( 25,178)( 26,180)( 27,179)( 28,175)( 29,177)( 30,176)( 31,172)( 32,174)
( 33,173)( 34,169)( 35,171)( 36,170)( 37,190)( 38,192)( 39,191)( 40,187)
( 41,189)( 42,188)( 43,184)( 44,186)( 45,185)( 46,181)( 47,183)( 48,182)
( 49, 97)( 50, 99)( 51, 98)( 52,100)( 53,102)( 54,101)( 55,103)( 56,105)
( 57,104)( 58,106)( 59,108)( 60,107)( 61,109)( 62,111)( 63,110)( 64,112)
( 65,114)( 66,113)( 67,115)( 68,117)( 69,116)( 70,118)( 71,120)( 72,119)
( 73,130)( 74,132)( 75,131)( 76,127)( 77,129)( 78,128)( 79,124)( 80,126)
( 81,125)( 82,121)( 83,123)( 84,122)( 85,142)( 86,144)( 87,143)( 88,139)
( 89,141)( 90,140)( 91,136)( 92,138)( 93,137)( 94,133)( 95,135)( 96,134);;
s1 := (  1,  2)(  4,  5)(  7,  8)( 10, 11)( 13, 17)( 14, 16)( 15, 18)( 19, 23)
( 20, 22)( 21, 24)( 25, 32)( 26, 31)( 27, 33)( 28, 35)( 29, 34)( 30, 36)
( 37, 47)( 38, 46)( 39, 48)( 40, 44)( 41, 43)( 42, 45)( 49, 62)( 50, 61)
( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 71)
( 59, 70)( 60, 72)( 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)(103,128)(104,127)(105,129)(106,131)
(107,130)(108,132)(109,137)(110,136)(111,138)(112,134)(113,133)(114,135)
(115,143)(116,142)(117,144)(118,140)(119,139)(120,141)(145,185)(146,184)
(147,186)(148,182)(149,181)(150,183)(151,191)(152,190)(153,192)(154,188)
(155,187)(156,189)(157,173)(158,172)(159,174)(160,170)(161,169)(162,171)
(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, 64)( 14, 65)( 15, 66)( 16, 61)
( 17, 62)( 18, 63)( 19, 70)( 20, 71)( 21, 72)( 22, 67)( 23, 68)( 24, 69)
( 25, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)( 32, 83)
( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 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)(109,160)(110,161)(111,162)(112,157)
(113,158)(114,159)(115,166)(116,167)(117,168)(118,163)(119,164)(120,165)
(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)(128,179)
(129,180)(130,175)(131,176)(132,177)(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*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope