Polytope of Type {2,8,3,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,3,4}*768
if this polytope has a name.
Group : SmallGroup(768,1090195)
Rank : 5
Schlafli Type : {2,8,3,4}
Number of vertices, edges, etc : 2, 16, 24, 12, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {2,4,3,4}*384b
4-fold quotients : {2,4,3,4}*192
8-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,103)( 4,104)( 5,106)( 6,105)( 7,100)( 8, 99)( 9,101)( 10,102)
( 11,111)( 12,112)( 13,114)( 14,113)( 15,108)( 16,107)( 17,109)( 18,110)
( 19,119)( 20,120)( 21,122)( 22,121)( 23,116)( 24,115)( 25,117)( 26,118)
( 27,127)( 28,128)( 29,130)( 30,129)( 31,124)( 32,123)( 33,125)( 34,126)
( 35,135)( 36,136)( 37,138)( 38,137)( 39,132)( 40,131)( 41,133)( 42,134)
( 43,143)( 44,144)( 45,146)( 46,145)( 47,140)( 48,139)( 49,141)( 50,142)
( 51,151)( 52,152)( 53,154)( 54,153)( 55,148)( 56,147)( 57,149)( 58,150)
( 59,159)( 60,160)( 61,162)( 62,161)( 63,156)( 64,155)( 65,157)( 66,158)
( 67,167)( 68,168)( 69,170)( 70,169)( 71,164)( 72,163)( 73,165)( 74,166)
( 75,175)( 76,176)( 77,178)( 78,177)( 79,172)( 80,171)( 81,173)( 82,174)
( 83,183)( 84,184)( 85,186)( 86,185)( 87,180)( 88,179)( 89,181)( 90,182)
( 91,191)( 92,192)( 93,194)( 94,193)( 95,188)( 96,187)( 97,189)( 98,190);;
s2 := ( 5, 6)( 7, 9)( 8, 10)( 11, 27)( 12, 28)( 13, 30)( 14, 29)( 15, 33)
( 16, 34)( 17, 31)( 18, 32)( 21, 22)( 23, 25)( 24, 26)( 35, 67)( 36, 68)
( 37, 70)( 38, 69)( 39, 73)( 40, 74)( 41, 71)( 42, 72)( 43, 91)( 44, 92)
( 45, 94)( 46, 93)( 47, 97)( 48, 98)( 49, 95)( 50, 96)( 51, 83)( 52, 84)
( 53, 86)( 54, 85)( 55, 89)( 56, 90)( 57, 87)( 58, 88)( 59, 75)( 60, 76)
( 61, 78)( 62, 77)( 63, 81)( 64, 82)( 65, 79)( 66, 80)( 99,100)(103,106)
(104,105)(107,124)(108,123)(109,125)(110,126)(111,130)(112,129)(113,128)
(114,127)(115,116)(119,122)(120,121)(131,164)(132,163)(133,165)(134,166)
(135,170)(136,169)(137,168)(138,167)(139,188)(140,187)(141,189)(142,190)
(143,194)(144,193)(145,192)(146,191)(147,180)(148,179)(149,181)(150,182)
(151,186)(152,185)(153,184)(154,183)(155,172)(156,171)(157,173)(158,174)
(159,178)(160,177)(161,176)(162,175);;
s3 := ( 3, 35)( 4, 36)( 5, 41)( 6, 42)( 7, 40)( 8, 39)( 9, 37)( 10, 38)
( 11, 51)( 12, 52)( 13, 57)( 14, 58)( 15, 56)( 16, 55)( 17, 53)( 18, 54)
( 19, 43)( 20, 44)( 21, 49)( 22, 50)( 23, 48)( 24, 47)( 25, 45)( 26, 46)
( 27, 59)( 28, 60)( 29, 65)( 30, 66)( 31, 64)( 32, 63)( 33, 61)( 34, 62)
( 69, 73)( 70, 74)( 71, 72)( 75, 83)( 76, 84)( 77, 89)( 78, 90)( 79, 88)
( 80, 87)( 81, 85)( 82, 86)( 93, 97)( 94, 98)( 95, 96)( 99,132)(100,131)
(101,138)(102,137)(103,135)(104,136)(105,134)(106,133)(107,148)(108,147)
(109,154)(110,153)(111,151)(112,152)(113,150)(114,149)(115,140)(116,139)
(117,146)(118,145)(119,143)(120,144)(121,142)(122,141)(123,156)(124,155)
(125,162)(126,161)(127,159)(128,160)(129,158)(130,157)(163,164)(165,170)
(166,169)(171,180)(172,179)(173,186)(174,185)(175,183)(176,184)(177,182)
(178,181)(187,188)(189,194)(190,193);;
s4 := ( 3, 19)( 4, 20)( 5, 21)( 6, 22)( 7, 23)( 8, 24)( 9, 25)( 10, 26)
( 11, 27)( 12, 28)( 13, 29)( 14, 30)( 15, 31)( 16, 32)( 17, 33)( 18, 34)
( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)( 40, 56)( 41, 57)( 42, 58)
( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)( 48, 64)( 49, 65)( 50, 66)
( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)( 72, 88)( 73, 89)( 74, 90)
( 75, 91)( 76, 92)( 77, 93)( 78, 94)( 79, 95)( 80, 96)( 81, 97)( 82, 98)
( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)(105,121)(106,122)
(107,123)(108,124)(109,125)(110,126)(111,127)(112,128)(113,129)(114,130)
(131,147)(132,148)(133,149)(134,150)(135,151)(136,152)(137,153)(138,154)
(139,155)(140,156)(141,157)(142,158)(143,159)(144,160)(145,161)(146,162)
(163,179)(164,180)(165,181)(166,182)(167,183)(168,184)(169,185)(170,186)
(171,187)(172,188)(173,189)(174,190)(175,191)(176,192)(177,193)(178,194);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s4*s3*s2*s4*s3*s2*s4*s3, s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*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(194)!(1,2);
s1 := Sym(194)!( 3,103)( 4,104)( 5,106)( 6,105)( 7,100)( 8, 99)( 9,101)
( 10,102)( 11,111)( 12,112)( 13,114)( 14,113)( 15,108)( 16,107)( 17,109)
( 18,110)( 19,119)( 20,120)( 21,122)( 22,121)( 23,116)( 24,115)( 25,117)
( 26,118)( 27,127)( 28,128)( 29,130)( 30,129)( 31,124)( 32,123)( 33,125)
( 34,126)( 35,135)( 36,136)( 37,138)( 38,137)( 39,132)( 40,131)( 41,133)
( 42,134)( 43,143)( 44,144)( 45,146)( 46,145)( 47,140)( 48,139)( 49,141)
( 50,142)( 51,151)( 52,152)( 53,154)( 54,153)( 55,148)( 56,147)( 57,149)
( 58,150)( 59,159)( 60,160)( 61,162)( 62,161)( 63,156)( 64,155)( 65,157)
( 66,158)( 67,167)( 68,168)( 69,170)( 70,169)( 71,164)( 72,163)( 73,165)
( 74,166)( 75,175)( 76,176)( 77,178)( 78,177)( 79,172)( 80,171)( 81,173)
( 82,174)( 83,183)( 84,184)( 85,186)( 86,185)( 87,180)( 88,179)( 89,181)
( 90,182)( 91,191)( 92,192)( 93,194)( 94,193)( 95,188)( 96,187)( 97,189)
( 98,190);
s2 := Sym(194)!( 5, 6)( 7, 9)( 8, 10)( 11, 27)( 12, 28)( 13, 30)( 14, 29)
( 15, 33)( 16, 34)( 17, 31)( 18, 32)( 21, 22)( 23, 25)( 24, 26)( 35, 67)
( 36, 68)( 37, 70)( 38, 69)( 39, 73)( 40, 74)( 41, 71)( 42, 72)( 43, 91)
( 44, 92)( 45, 94)( 46, 93)( 47, 97)( 48, 98)( 49, 95)( 50, 96)( 51, 83)
( 52, 84)( 53, 86)( 54, 85)( 55, 89)( 56, 90)( 57, 87)( 58, 88)( 59, 75)
( 60, 76)( 61, 78)( 62, 77)( 63, 81)( 64, 82)( 65, 79)( 66, 80)( 99,100)
(103,106)(104,105)(107,124)(108,123)(109,125)(110,126)(111,130)(112,129)
(113,128)(114,127)(115,116)(119,122)(120,121)(131,164)(132,163)(133,165)
(134,166)(135,170)(136,169)(137,168)(138,167)(139,188)(140,187)(141,189)
(142,190)(143,194)(144,193)(145,192)(146,191)(147,180)(148,179)(149,181)
(150,182)(151,186)(152,185)(153,184)(154,183)(155,172)(156,171)(157,173)
(158,174)(159,178)(160,177)(161,176)(162,175);
s3 := Sym(194)!( 3, 35)( 4, 36)( 5, 41)( 6, 42)( 7, 40)( 8, 39)( 9, 37)
( 10, 38)( 11, 51)( 12, 52)( 13, 57)( 14, 58)( 15, 56)( 16, 55)( 17, 53)
( 18, 54)( 19, 43)( 20, 44)( 21, 49)( 22, 50)( 23, 48)( 24, 47)( 25, 45)
( 26, 46)( 27, 59)( 28, 60)( 29, 65)( 30, 66)( 31, 64)( 32, 63)( 33, 61)
( 34, 62)( 69, 73)( 70, 74)( 71, 72)( 75, 83)( 76, 84)( 77, 89)( 78, 90)
( 79, 88)( 80, 87)( 81, 85)( 82, 86)( 93, 97)( 94, 98)( 95, 96)( 99,132)
(100,131)(101,138)(102,137)(103,135)(104,136)(105,134)(106,133)(107,148)
(108,147)(109,154)(110,153)(111,151)(112,152)(113,150)(114,149)(115,140)
(116,139)(117,146)(118,145)(119,143)(120,144)(121,142)(122,141)(123,156)
(124,155)(125,162)(126,161)(127,159)(128,160)(129,158)(130,157)(163,164)
(165,170)(166,169)(171,180)(172,179)(173,186)(174,185)(175,183)(176,184)
(177,182)(178,181)(187,188)(189,194)(190,193);
s4 := Sym(194)!( 3, 19)( 4, 20)( 5, 21)( 6, 22)( 7, 23)( 8, 24)( 9, 25)
( 10, 26)( 11, 27)( 12, 28)( 13, 29)( 14, 30)( 15, 31)( 16, 32)( 17, 33)
( 18, 34)( 35, 51)( 36, 52)( 37, 53)( 38, 54)( 39, 55)( 40, 56)( 41, 57)
( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)( 48, 64)( 49, 65)
( 50, 66)( 67, 83)( 68, 84)( 69, 85)( 70, 86)( 71, 87)( 72, 88)( 73, 89)
( 74, 90)( 75, 91)( 76, 92)( 77, 93)( 78, 94)( 79, 95)( 80, 96)( 81, 97)
( 82, 98)( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)(105,121)
(106,122)(107,123)(108,124)(109,125)(110,126)(111,127)(112,128)(113,129)
(114,130)(131,147)(132,148)(133,149)(134,150)(135,151)(136,152)(137,153)
(138,154)(139,155)(140,156)(141,157)(142,158)(143,159)(144,160)(145,161)
(146,162)(163,179)(164,180)(165,181)(166,182)(167,183)(168,184)(169,185)
(170,186)(171,187)(172,188)(173,189)(174,190)(175,191)(176,192)(177,193)
(178,194);
poly := sub<Sym(194)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s2*s4*s3*s2*s4*s3,
s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope