Polytope of Type {2,224}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,224}*896
if this polytope has a name.
Group : SmallGroup(896,1887)
Rank : 3
Schlafli Type : {2,224}
Number of vertices, edges, etc : 2, 224, 224
Order of s0s1s2 : 224
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,224,2} of size 1792
Vertex Figure Of :
{2,2,224} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,112}*448
4-fold quotients : {2,56}*224
7-fold quotients : {2,32}*128
8-fold quotients : {2,28}*112
14-fold quotients : {2,16}*64
16-fold quotients : {2,14}*56
28-fold quotients : {2,8}*32
32-fold quotients : {2,7}*28
56-fold quotients : {2,4}*16
112-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,224}*1792a, {2,448}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 17, 24)( 18, 30)
( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 31, 45)( 32, 51)( 33, 50)
( 34, 49)( 35, 48)( 36, 47)( 37, 46)( 38, 52)( 39, 58)( 40, 57)( 41, 56)
( 42, 55)( 43, 54)( 44, 53)( 59, 87)( 60, 93)( 61, 92)( 62, 91)( 63, 90)
( 64, 89)( 65, 88)( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)
( 72, 95)( 73,108)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)( 79,109)
( 80,101)( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102)(115,171)
(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)(122,178)(123,184)
(124,183)(125,182)(126,181)(127,180)(128,179)(129,192)(130,198)(131,197)
(132,196)(133,195)(134,194)(135,193)(136,185)(137,191)(138,190)(139,189)
(140,188)(141,187)(142,186)(143,213)(144,219)(145,218)(146,217)(147,216)
(148,215)(149,214)(150,220)(151,226)(152,225)(153,224)(154,223)(155,222)
(156,221)(157,199)(158,205)(159,204)(160,203)(161,202)(162,201)(163,200)
(164,206)(165,212)(166,211)(167,210)(168,209)(169,208)(170,207);;
s2 := ( 3,116)( 4,115)( 5,121)( 6,120)( 7,119)( 8,118)( 9,117)( 10,123)
( 11,122)( 12,128)( 13,127)( 14,126)( 15,125)( 16,124)( 17,137)( 18,136)
( 19,142)( 20,141)( 21,140)( 22,139)( 23,138)( 24,130)( 25,129)( 26,135)
( 27,134)( 28,133)( 29,132)( 30,131)( 31,158)( 32,157)( 33,163)( 34,162)
( 35,161)( 36,160)( 37,159)( 38,165)( 39,164)( 40,170)( 41,169)( 42,168)
( 43,167)( 44,166)( 45,144)( 46,143)( 47,149)( 48,148)( 49,147)( 50,146)
( 51,145)( 52,151)( 53,150)( 54,156)( 55,155)( 56,154)( 57,153)( 58,152)
( 59,200)( 60,199)( 61,205)( 62,204)( 63,203)( 64,202)( 65,201)( 66,207)
( 67,206)( 68,212)( 69,211)( 70,210)( 71,209)( 72,208)( 73,221)( 74,220)
( 75,226)( 76,225)( 77,224)( 78,223)( 79,222)( 80,214)( 81,213)( 82,219)
( 83,218)( 84,217)( 85,216)( 86,215)( 87,172)( 88,171)( 89,177)( 90,176)
( 91,175)( 92,174)( 93,173)( 94,179)( 95,178)( 96,184)( 97,183)( 98,182)
( 99,181)(100,180)(101,193)(102,192)(103,198)(104,197)(105,196)(106,195)
(107,194)(108,186)(109,185)(110,191)(111,190)(112,189)(113,188)(114,187);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(226)!(1,2);
s1 := Sym(226)!( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 17, 24)
( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 31, 45)( 32, 51)
( 33, 50)( 34, 49)( 35, 48)( 36, 47)( 37, 46)( 38, 52)( 39, 58)( 40, 57)
( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 59, 87)( 60, 93)( 61, 92)( 62, 91)
( 63, 90)( 64, 89)( 65, 88)( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)
( 71, 96)( 72, 95)( 73,108)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)
( 79,109)( 80,101)( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102)
(115,171)(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)(122,178)
(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,192)(130,198)
(131,197)(132,196)(133,195)(134,194)(135,193)(136,185)(137,191)(138,190)
(139,189)(140,188)(141,187)(142,186)(143,213)(144,219)(145,218)(146,217)
(147,216)(148,215)(149,214)(150,220)(151,226)(152,225)(153,224)(154,223)
(155,222)(156,221)(157,199)(158,205)(159,204)(160,203)(161,202)(162,201)
(163,200)(164,206)(165,212)(166,211)(167,210)(168,209)(169,208)(170,207);
s2 := Sym(226)!( 3,116)( 4,115)( 5,121)( 6,120)( 7,119)( 8,118)( 9,117)
( 10,123)( 11,122)( 12,128)( 13,127)( 14,126)( 15,125)( 16,124)( 17,137)
( 18,136)( 19,142)( 20,141)( 21,140)( 22,139)( 23,138)( 24,130)( 25,129)
( 26,135)( 27,134)( 28,133)( 29,132)( 30,131)( 31,158)( 32,157)( 33,163)
( 34,162)( 35,161)( 36,160)( 37,159)( 38,165)( 39,164)( 40,170)( 41,169)
( 42,168)( 43,167)( 44,166)( 45,144)( 46,143)( 47,149)( 48,148)( 49,147)
( 50,146)( 51,145)( 52,151)( 53,150)( 54,156)( 55,155)( 56,154)( 57,153)
( 58,152)( 59,200)( 60,199)( 61,205)( 62,204)( 63,203)( 64,202)( 65,201)
( 66,207)( 67,206)( 68,212)( 69,211)( 70,210)( 71,209)( 72,208)( 73,221)
( 74,220)( 75,226)( 76,225)( 77,224)( 78,223)( 79,222)( 80,214)( 81,213)
( 82,219)( 83,218)( 84,217)( 85,216)( 86,215)( 87,172)( 88,171)( 89,177)
( 90,176)( 91,175)( 92,174)( 93,173)( 94,179)( 95,178)( 96,184)( 97,183)
( 98,182)( 99,181)(100,180)(101,193)(102,192)(103,198)(104,197)(105,196)
(106,195)(107,194)(108,186)(109,185)(110,191)(111,190)(112,189)(113,188)
(114,187);
poly := sub<Sym(226)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s1*s0*s1, s0*s2*s0*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*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*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope