Polytope of Type {2,12,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,16}*768a
if this polytope has a name.
Group : SmallGroup(768,323305)
Rank : 4
Schlafli Type : {2,12,16}
Number of vertices, edges, etc : 2, 12, 96, 16
Order of s0s1s2s3 : 48
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 : {2,12,8}*384a, {2,6,16}*384
3-fold quotients : {2,4,16}*256a
4-fold quotients : {2,12,4}*192a, {2,6,8}*192
6-fold quotients : {2,4,8}*128a, {2,2,16}*128
8-fold quotients : {2,12,2}*96, {2,6,4}*96a
12-fold quotients : {2,4,4}*64, {2,2,8}*64
16-fold quotients : {2,6,2}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32
32-fold quotients : {2,3,2}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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);;
s2 := ( 3, 4)( 6, 7)( 9, 13)( 10, 12)( 11, 14)( 15, 16)( 18, 19)( 21, 25)
( 22, 24)( 23, 26)( 27, 34)( 28, 33)( 29, 35)( 30, 37)( 31, 36)( 32, 38)
( 39, 46)( 40, 45)( 41, 47)( 42, 49)( 43, 48)( 44, 50)( 51, 64)( 52, 63)
( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 73)( 58, 72)( 59, 74)( 60, 70)
( 61, 69)( 62, 71)( 75, 94)( 76, 93)( 77, 95)( 78, 97)( 79, 96)( 80, 98)
( 81, 88)( 82, 87)( 83, 89)( 84, 91)( 85, 90)( 86, 92)( 99,124)(100,123)
(101,125)(102,127)(103,126)(104,128)(105,133)(106,132)(107,134)(108,130)
(109,129)(110,131)(111,136)(112,135)(113,137)(114,139)(115,138)(116,140)
(117,145)(118,144)(119,146)(120,142)(121,141)(122,143)(147,184)(148,183)
(149,185)(150,187)(151,186)(152,188)(153,193)(154,192)(155,194)(156,190)
(157,189)(158,191)(159,172)(160,171)(161,173)(162,175)(163,174)(164,176)
(165,181)(166,180)(167,182)(168,178)(169,177)(170,179);;
s3 := ( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,108)( 10,109)
( 11,110)( 12,105)( 13,106)( 14,107)( 15,111)( 16,112)( 17,113)( 18,114)
( 19,115)( 20,116)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)( 26,119)
( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)( 34,124)
( 35,125)( 36,126)( 37,127)( 38,128)( 39,141)( 40,142)( 41,143)( 42,144)
( 43,145)( 44,146)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)( 50,140)
( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,156)( 58,157)
( 59,158)( 60,153)( 61,154)( 62,155)( 63,159)( 64,160)( 65,161)( 66,162)
( 67,163)( 68,164)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)( 74,167)
( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)( 82,172)
( 83,173)( 84,174)( 85,175)( 86,176)( 87,189)( 88,190)( 89,191)( 90,192)
( 91,193)( 92,194)( 93,183)( 94,184)( 95,185)( 96,186)( 97,187)( 98,188);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := 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);
s2 := Sym(194)!( 3, 4)( 6, 7)( 9, 13)( 10, 12)( 11, 14)( 15, 16)( 18, 19)
( 21, 25)( 22, 24)( 23, 26)( 27, 34)( 28, 33)( 29, 35)( 30, 37)( 31, 36)
( 32, 38)( 39, 46)( 40, 45)( 41, 47)( 42, 49)( 43, 48)( 44, 50)( 51, 64)
( 52, 63)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 73)( 58, 72)( 59, 74)
( 60, 70)( 61, 69)( 62, 71)( 75, 94)( 76, 93)( 77, 95)( 78, 97)( 79, 96)
( 80, 98)( 81, 88)( 82, 87)( 83, 89)( 84, 91)( 85, 90)( 86, 92)( 99,124)
(100,123)(101,125)(102,127)(103,126)(104,128)(105,133)(106,132)(107,134)
(108,130)(109,129)(110,131)(111,136)(112,135)(113,137)(114,139)(115,138)
(116,140)(117,145)(118,144)(119,146)(120,142)(121,141)(122,143)(147,184)
(148,183)(149,185)(150,187)(151,186)(152,188)(153,193)(154,192)(155,194)
(156,190)(157,189)(158,191)(159,172)(160,171)(161,173)(162,175)(163,174)
(164,176)(165,181)(166,180)(167,182)(168,178)(169,177)(170,179);
s3 := Sym(194)!( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,108)
( 10,109)( 11,110)( 12,105)( 13,106)( 14,107)( 15,111)( 16,112)( 17,113)
( 18,114)( 19,115)( 20,116)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)
( 26,119)( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)
( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,141)( 40,142)( 41,143)
( 42,144)( 43,145)( 44,146)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)
( 50,140)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,156)
( 58,157)( 59,158)( 60,153)( 61,154)( 62,155)( 63,159)( 64,160)( 65,161)
( 66,162)( 67,163)( 68,164)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)
( 74,167)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)
( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,189)( 88,190)( 89,191)
( 90,192)( 91,193)( 92,194)( 93,183)( 94,184)( 95,185)( 96,186)( 97,187)
( 98,188);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope