Polytope of Type {2,12,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4,4}*768
if this polytope has a name.
Group : SmallGroup(768,336974)
Rank : 5
Schlafli Type : {2,12,4,4}
Number of vertices, edges, etc : 2, 12, 24, 8, 4
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 : {2,12,4,2}*384a, {2,12,2,4}*384, {2,6,4,4}*384
3-fold quotients : {2,4,4,4}*256
4-fold quotients : {2,12,2,2}*192, {2,6,2,4}*192, {2,6,4,2}*192a
6-fold quotients : {2,2,4,4}*128, {2,4,4,2}*128, {2,4,2,4}*128
8-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
12-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64, {2,4,2,2}*64
16-fold quotients : {2,3,2,2}*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 := ( 3,123)( 4,125)( 5,124)( 6,126)( 7,128)( 8,127)( 9,129)( 10,131)
( 11,130)( 12,132)( 13,134)( 14,133)( 15,135)( 16,137)( 17,136)( 18,138)
( 19,140)( 20,139)( 21,141)( 22,143)( 23,142)( 24,144)( 25,146)( 26,145)
( 27, 99)( 28,101)( 29,100)( 30,102)( 31,104)( 32,103)( 33,105)( 34,107)
( 35,106)( 36,108)( 37,110)( 38,109)( 39,111)( 40,113)( 41,112)( 42,114)
( 43,116)( 44,115)( 45,117)( 46,119)( 47,118)( 48,120)( 49,122)( 50,121)
( 51,174)( 52,176)( 53,175)( 54,171)( 55,173)( 56,172)( 57,180)( 58,182)
( 59,181)( 60,177)( 61,179)( 62,178)( 63,186)( 64,188)( 65,187)( 66,183)
( 67,185)( 68,184)( 69,192)( 70,194)( 71,193)( 72,189)( 73,191)( 74,190)
( 75,150)( 76,152)( 77,151)( 78,147)( 79,149)( 80,148)( 81,156)( 82,158)
( 83,157)( 84,153)( 85,155)( 86,154)( 87,162)( 88,164)( 89,163)( 90,159)
( 91,161)( 92,160)( 93,168)( 94,170)( 95,169)( 96,165)( 97,167)( 98,166);;
s2 := ( 3, 52)( 4, 51)( 5, 53)( 6, 55)( 7, 54)( 8, 56)( 9, 58)( 10, 57)
( 11, 59)( 12, 61)( 13, 60)( 14, 62)( 15, 64)( 16, 63)( 17, 65)( 18, 67)
( 19, 66)( 20, 68)( 21, 70)( 22, 69)( 23, 71)( 24, 73)( 25, 72)( 26, 74)
( 27, 76)( 28, 75)( 29, 77)( 30, 79)( 31, 78)( 32, 80)( 33, 82)( 34, 81)
( 35, 83)( 36, 85)( 37, 84)( 38, 86)( 39, 88)( 40, 87)( 41, 89)( 42, 91)
( 43, 90)( 44, 92)( 45, 94)( 46, 93)( 47, 95)( 48, 97)( 49, 96)( 50, 98)
( 99,148)(100,147)(101,149)(102,151)(103,150)(104,152)(105,154)(106,153)
(107,155)(108,157)(109,156)(110,158)(111,160)(112,159)(113,161)(114,163)
(115,162)(116,164)(117,166)(118,165)(119,167)(120,169)(121,168)(122,170)
(123,172)(124,171)(125,173)(126,175)(127,174)(128,176)(129,178)(130,177)
(131,179)(132,181)(133,180)(134,182)(135,184)(136,183)(137,185)(138,187)
(139,186)(140,188)(141,190)(142,189)(143,191)(144,193)(145,192)(146,194);;
s3 := ( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 43)( 32, 44)( 33, 45)( 34, 46)
( 35, 47)( 36, 48)( 37, 49)( 38, 50)( 51, 57)( 52, 58)( 53, 59)( 54, 60)
( 55, 61)( 56, 62)( 63, 69)( 64, 70)( 65, 71)( 66, 72)( 67, 73)( 68, 74)
( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 87)( 82, 88)
( 83, 89)( 84, 90)( 85, 91)( 86, 92)( 99,111)(100,112)(101,113)(102,114)
(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(109,121)(110,122)
(147,165)(148,166)(149,167)(150,168)(151,169)(152,170)(153,159)(154,160)
(155,161)(156,162)(157,163)(158,164)(171,177)(172,178)(173,179)(174,180)
(175,181)(176,182)(183,189)(184,190)(185,191)(186,192)(187,193)(188,194);;
s4 := ( 3, 27)( 4, 28)( 5, 29)( 6, 30)( 7, 31)( 8, 32)( 9, 33)( 10, 34)
( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)( 16, 40)( 17, 41)( 18, 42)
( 19, 43)( 20, 44)( 21, 45)( 22, 46)( 23, 47)( 24, 48)( 25, 49)( 26, 50)
( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)( 57, 81)( 58, 82)
( 59, 83)( 60, 84)( 61, 85)( 62, 86)( 63, 87)( 64, 88)( 65, 89)( 66, 90)
( 67, 91)( 68, 92)( 69, 93)( 70, 94)( 71, 95)( 72, 96)( 73, 97)( 74, 98)
( 99,123)(100,124)(101,125)(102,126)(103,127)(104,128)(105,129)(106,130)
(107,131)(108,132)(109,133)(110,134)(111,135)(112,136)(113,137)(114,138)
(115,139)(116,140)(117,141)(118,142)(119,143)(120,144)(121,145)(122,146)
(147,171)(148,172)(149,173)(150,174)(151,175)(152,176)(153,177)(154,178)
(155,179)(156,180)(157,181)(158,182)(159,183)(160,184)(161,185)(162,186)
(163,187)(164,188)(165,189)(166,190)(167,191)(168,192)(169,193)(170,194);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
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(194)!(1,2);
s1 := Sym(194)!( 3,123)( 4,125)( 5,124)( 6,126)( 7,128)( 8,127)( 9,129)
( 10,131)( 11,130)( 12,132)( 13,134)( 14,133)( 15,135)( 16,137)( 17,136)
( 18,138)( 19,140)( 20,139)( 21,141)( 22,143)( 23,142)( 24,144)( 25,146)
( 26,145)( 27, 99)( 28,101)( 29,100)( 30,102)( 31,104)( 32,103)( 33,105)
( 34,107)( 35,106)( 36,108)( 37,110)( 38,109)( 39,111)( 40,113)( 41,112)
( 42,114)( 43,116)( 44,115)( 45,117)( 46,119)( 47,118)( 48,120)( 49,122)
( 50,121)( 51,174)( 52,176)( 53,175)( 54,171)( 55,173)( 56,172)( 57,180)
( 58,182)( 59,181)( 60,177)( 61,179)( 62,178)( 63,186)( 64,188)( 65,187)
( 66,183)( 67,185)( 68,184)( 69,192)( 70,194)( 71,193)( 72,189)( 73,191)
( 74,190)( 75,150)( 76,152)( 77,151)( 78,147)( 79,149)( 80,148)( 81,156)
( 82,158)( 83,157)( 84,153)( 85,155)( 86,154)( 87,162)( 88,164)( 89,163)
( 90,159)( 91,161)( 92,160)( 93,168)( 94,170)( 95,169)( 96,165)( 97,167)
( 98,166);
s2 := Sym(194)!( 3, 52)( 4, 51)( 5, 53)( 6, 55)( 7, 54)( 8, 56)( 9, 58)
( 10, 57)( 11, 59)( 12, 61)( 13, 60)( 14, 62)( 15, 64)( 16, 63)( 17, 65)
( 18, 67)( 19, 66)( 20, 68)( 21, 70)( 22, 69)( 23, 71)( 24, 73)( 25, 72)
( 26, 74)( 27, 76)( 28, 75)( 29, 77)( 30, 79)( 31, 78)( 32, 80)( 33, 82)
( 34, 81)( 35, 83)( 36, 85)( 37, 84)( 38, 86)( 39, 88)( 40, 87)( 41, 89)
( 42, 91)( 43, 90)( 44, 92)( 45, 94)( 46, 93)( 47, 95)( 48, 97)( 49, 96)
( 50, 98)( 99,148)(100,147)(101,149)(102,151)(103,150)(104,152)(105,154)
(106,153)(107,155)(108,157)(109,156)(110,158)(111,160)(112,159)(113,161)
(114,163)(115,162)(116,164)(117,166)(118,165)(119,167)(120,169)(121,168)
(122,170)(123,172)(124,171)(125,173)(126,175)(127,174)(128,176)(129,178)
(130,177)(131,179)(132,181)(133,180)(134,182)(135,184)(136,183)(137,185)
(138,187)(139,186)(140,188)(141,190)(142,189)(143,191)(144,193)(145,192)
(146,194);
s3 := Sym(194)!( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 43)( 32, 44)( 33, 45)
( 34, 46)( 35, 47)( 36, 48)( 37, 49)( 38, 50)( 51, 57)( 52, 58)( 53, 59)
( 54, 60)( 55, 61)( 56, 62)( 63, 69)( 64, 70)( 65, 71)( 66, 72)( 67, 73)
( 68, 74)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 87)
( 82, 88)( 83, 89)( 84, 90)( 85, 91)( 86, 92)( 99,111)(100,112)(101,113)
(102,114)(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(109,121)
(110,122)(147,165)(148,166)(149,167)(150,168)(151,169)(152,170)(153,159)
(154,160)(155,161)(156,162)(157,163)(158,164)(171,177)(172,178)(173,179)
(174,180)(175,181)(176,182)(183,189)(184,190)(185,191)(186,192)(187,193)
(188,194);
s4 := Sym(194)!( 3, 27)( 4, 28)( 5, 29)( 6, 30)( 7, 31)( 8, 32)( 9, 33)
( 10, 34)( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)( 16, 40)( 17, 41)
( 18, 42)( 19, 43)( 20, 44)( 21, 45)( 22, 46)( 23, 47)( 24, 48)( 25, 49)
( 26, 50)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)( 57, 81)
( 58, 82)( 59, 83)( 60, 84)( 61, 85)( 62, 86)( 63, 87)( 64, 88)( 65, 89)
( 66, 90)( 67, 91)( 68, 92)( 69, 93)( 70, 94)( 71, 95)( 72, 96)( 73, 97)
( 74, 98)( 99,123)(100,124)(101,125)(102,126)(103,127)(104,128)(105,129)
(106,130)(107,131)(108,132)(109,133)(110,134)(111,135)(112,136)(113,137)
(114,138)(115,139)(116,140)(117,141)(118,142)(119,143)(120,144)(121,145)
(122,146)(147,171)(148,172)(149,173)(150,174)(151,175)(152,176)(153,177)
(154,178)(155,179)(156,180)(157,181)(158,182)(159,183)(160,184)(161,185)
(162,186)(163,187)(164,188)(165,189)(166,190)(167,191)(168,192)(169,193)
(170,194);
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, 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