Polytope of Type {2,4,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,6}*768d
if this polytope has a name.
Group : SmallGroup(768,1090146)
Rank : 5
Schlafli Type : {2,4,4,6}
Number of vertices, edges, etc : 2, 4, 16, 24, 12
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 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 : {2,4,4,3}*384b, {2,2,4,6}*384
4-fold quotients : {2,4,2,6}*192, {2,2,4,3}*192, {2,2,4,6}*192b, {2,2,4,6}*192c
8-fold quotients : {2,4,2,3}*96, {2,2,4,3}*96, {2,2,2,6}*96
12-fold quotients : {2,4,2,2}*64
16-fold quotients : {2,2,2,3}*48
24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 33, 93)( 34, 94)
( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 75)( 40, 76)( 41, 77)( 42, 78)
( 43, 79)( 44, 80)( 45, 81)( 46, 82)( 47, 83)( 48, 84)( 49, 85)( 50, 86)
( 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)
(123,183)(124,184)(125,185)(126,186)(127,187)(128,188)(129,189)(130,190)
(131,191)(132,192)(133,193)(134,194)(135,171)(136,172)(137,173)(138,174)
(139,175)(140,176)(141,177)(142,178)(143,179)(144,180)(145,181)(146,182);;
s2 := ( 3, 29)( 4, 30)( 5, 27)( 6, 28)( 7, 33)( 8, 34)( 9, 31)( 10, 32)
( 11, 37)( 12, 38)( 13, 35)( 14, 36)( 15, 41)( 16, 42)( 17, 39)( 18, 40)
( 19, 45)( 20, 46)( 21, 43)( 22, 44)( 23, 49)( 24, 50)( 25, 47)( 26, 48)
( 51, 77)( 52, 78)( 53, 75)( 54, 76)( 55, 81)( 56, 82)( 57, 79)( 58, 80)
( 59, 85)( 60, 86)( 61, 83)( 62, 84)( 63, 89)( 64, 90)( 65, 87)( 66, 88)
( 67, 93)( 68, 94)( 69, 91)( 70, 92)( 71, 97)( 72, 98)( 73, 95)( 74, 96)
( 99,125)(100,126)(101,123)(102,124)(103,129)(104,130)(105,127)(106,128)
(107,133)(108,134)(109,131)(110,132)(111,137)(112,138)(113,135)(114,136)
(115,141)(116,142)(117,139)(118,140)(119,145)(120,146)(121,143)(122,144)
(147,173)(148,174)(149,171)(150,172)(151,177)(152,178)(153,175)(154,176)
(155,181)(156,182)(157,179)(158,180)(159,185)(160,186)(161,183)(162,184)
(163,189)(164,190)(165,187)(166,188)(167,193)(168,194)(169,191)(170,192);;
s3 := ( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 23)( 20, 25)
( 21, 24)( 22, 26)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 40, 41)
( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 52, 53)( 55, 59)( 56, 61)( 57, 60)
( 58, 62)( 64, 65)( 67, 71)( 68, 73)( 69, 72)( 70, 74)( 76, 77)( 79, 83)
( 80, 85)( 81, 84)( 82, 86)( 88, 89)( 91, 95)( 92, 97)( 93, 96)( 94, 98)
(100,101)(103,107)(104,109)(105,108)(106,110)(112,113)(115,119)(116,121)
(117,120)(118,122)(124,125)(127,131)(128,133)(129,132)(130,134)(136,137)
(139,143)(140,145)(141,144)(142,146)(148,149)(151,155)(152,157)(153,156)
(154,158)(160,161)(163,167)(164,169)(165,168)(166,170)(172,173)(175,179)
(176,181)(177,180)(178,182)(184,185)(187,191)(188,193)(189,192)(190,194);;
s4 := ( 3,107)( 4,110)( 5,109)( 6,108)( 7,103)( 8,106)( 9,105)( 10,104)
( 11, 99)( 12,102)( 13,101)( 14,100)( 15,119)( 16,122)( 17,121)( 18,120)
( 19,115)( 20,118)( 21,117)( 22,116)( 23,111)( 24,114)( 25,113)( 26,112)
( 27,131)( 28,134)( 29,133)( 30,132)( 31,127)( 32,130)( 33,129)( 34,128)
( 35,123)( 36,126)( 37,125)( 38,124)( 39,143)( 40,146)( 41,145)( 42,144)
( 43,139)( 44,142)( 45,141)( 46,140)( 47,135)( 48,138)( 49,137)( 50,136)
( 51,155)( 52,158)( 53,157)( 54,156)( 55,151)( 56,154)( 57,153)( 58,152)
( 59,147)( 60,150)( 61,149)( 62,148)( 63,167)( 64,170)( 65,169)( 66,168)
( 67,163)( 68,166)( 69,165)( 70,164)( 71,159)( 72,162)( 73,161)( 74,160)
( 75,179)( 76,182)( 77,181)( 78,180)( 79,175)( 80,178)( 81,177)( 82,176)
( 83,171)( 84,174)( 85,173)( 86,172)( 87,191)( 88,194)( 89,193)( 90,192)
( 91,187)( 92,190)( 93,189)( 94,188)( 95,183)( 96,186)( 97,185)( 98,184);;
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 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, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 91)( 32, 92)( 33, 93)
( 34, 94)( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 75)( 40, 76)( 41, 77)
( 42, 78)( 43, 79)( 44, 80)( 45, 81)( 46, 82)( 47, 83)( 48, 84)( 49, 85)
( 50, 86)( 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)(123,183)(124,184)(125,185)(126,186)(127,187)(128,188)(129,189)
(130,190)(131,191)(132,192)(133,193)(134,194)(135,171)(136,172)(137,173)
(138,174)(139,175)(140,176)(141,177)(142,178)(143,179)(144,180)(145,181)
(146,182);
s2 := Sym(194)!( 3, 29)( 4, 30)( 5, 27)( 6, 28)( 7, 33)( 8, 34)( 9, 31)
( 10, 32)( 11, 37)( 12, 38)( 13, 35)( 14, 36)( 15, 41)( 16, 42)( 17, 39)
( 18, 40)( 19, 45)( 20, 46)( 21, 43)( 22, 44)( 23, 49)( 24, 50)( 25, 47)
( 26, 48)( 51, 77)( 52, 78)( 53, 75)( 54, 76)( 55, 81)( 56, 82)( 57, 79)
( 58, 80)( 59, 85)( 60, 86)( 61, 83)( 62, 84)( 63, 89)( 64, 90)( 65, 87)
( 66, 88)( 67, 93)( 68, 94)( 69, 91)( 70, 92)( 71, 97)( 72, 98)( 73, 95)
( 74, 96)( 99,125)(100,126)(101,123)(102,124)(103,129)(104,130)(105,127)
(106,128)(107,133)(108,134)(109,131)(110,132)(111,137)(112,138)(113,135)
(114,136)(115,141)(116,142)(117,139)(118,140)(119,145)(120,146)(121,143)
(122,144)(147,173)(148,174)(149,171)(150,172)(151,177)(152,178)(153,175)
(154,176)(155,181)(156,182)(157,179)(158,180)(159,185)(160,186)(161,183)
(162,184)(163,189)(164,190)(165,187)(166,188)(167,193)(168,194)(169,191)
(170,192);
s3 := Sym(194)!( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 23)
( 20, 25)( 21, 24)( 22, 26)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)
( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 52, 53)( 55, 59)( 56, 61)
( 57, 60)( 58, 62)( 64, 65)( 67, 71)( 68, 73)( 69, 72)( 70, 74)( 76, 77)
( 79, 83)( 80, 85)( 81, 84)( 82, 86)( 88, 89)( 91, 95)( 92, 97)( 93, 96)
( 94, 98)(100,101)(103,107)(104,109)(105,108)(106,110)(112,113)(115,119)
(116,121)(117,120)(118,122)(124,125)(127,131)(128,133)(129,132)(130,134)
(136,137)(139,143)(140,145)(141,144)(142,146)(148,149)(151,155)(152,157)
(153,156)(154,158)(160,161)(163,167)(164,169)(165,168)(166,170)(172,173)
(175,179)(176,181)(177,180)(178,182)(184,185)(187,191)(188,193)(189,192)
(190,194);
s4 := Sym(194)!( 3,107)( 4,110)( 5,109)( 6,108)( 7,103)( 8,106)( 9,105)
( 10,104)( 11, 99)( 12,102)( 13,101)( 14,100)( 15,119)( 16,122)( 17,121)
( 18,120)( 19,115)( 20,118)( 21,117)( 22,116)( 23,111)( 24,114)( 25,113)
( 26,112)( 27,131)( 28,134)( 29,133)( 30,132)( 31,127)( 32,130)( 33,129)
( 34,128)( 35,123)( 36,126)( 37,125)( 38,124)( 39,143)( 40,146)( 41,145)
( 42,144)( 43,139)( 44,142)( 45,141)( 46,140)( 47,135)( 48,138)( 49,137)
( 50,136)( 51,155)( 52,158)( 53,157)( 54,156)( 55,151)( 56,154)( 57,153)
( 58,152)( 59,147)( 60,150)( 61,149)( 62,148)( 63,167)( 64,170)( 65,169)
( 66,168)( 67,163)( 68,166)( 69,165)( 70,164)( 71,159)( 72,162)( 73,161)
( 74,160)( 75,179)( 76,182)( 77,181)( 78,180)( 79,175)( 80,178)( 81,177)
( 82,176)( 83,171)( 84,174)( 85,173)( 86,172)( 87,191)( 88,194)( 89,193)
( 90,192)( 91,187)( 92,190)( 93,189)( 94,188)( 95,183)( 96,186)( 97,185)
( 98,184);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope