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