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# Polytope of Type {206,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {206,2}*824
if this polytope has a name.
Group : SmallGroup(824,11)
Rank : 3
Schlafli Type : {206,2}
Number of vertices, edges, etc : 206, 206, 2
Order of s0s1s2 : 206
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{206,2,2} of size 1648
Vertex Figure Of :
{2,206,2} of size 1648
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {103,2}*412
103-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {206,4}*1648, {412,2}*1648
Permutation Representation (GAP) :
```s0 := (  2,103)(  3,102)(  4,101)(  5,100)(  6, 99)(  7, 98)(  8, 97)(  9, 96)
( 10, 95)( 11, 94)( 12, 93)( 13, 92)( 14, 91)( 15, 90)( 16, 89)( 17, 88)
( 18, 87)( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 80)
( 26, 79)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 74)( 32, 73)( 33, 72)
( 34, 71)( 35, 70)( 36, 69)( 37, 68)( 38, 67)( 39, 66)( 40, 65)( 41, 64)
( 42, 63)( 43, 62)( 44, 61)( 45, 60)( 46, 59)( 47, 58)( 48, 57)( 49, 56)
( 50, 55)( 51, 54)( 52, 53)(105,206)(106,205)(107,204)(108,203)(109,202)
(110,201)(111,200)(112,199)(113,198)(114,197)(115,196)(116,195)(117,194)
(118,193)(119,192)(120,191)(121,190)(122,189)(123,188)(124,187)(125,186)
(126,185)(127,184)(128,183)(129,182)(130,181)(131,180)(132,179)(133,178)
(134,177)(135,176)(136,175)(137,174)(138,173)(139,172)(140,171)(141,170)
(142,169)(143,168)(144,167)(145,166)(146,165)(147,164)(148,163)(149,162)
(150,161)(151,160)(152,159)(153,158)(154,157)(155,156);;
s1 := (  1,105)(  2,104)(  3,206)(  4,205)(  5,204)(  6,203)(  7,202)(  8,201)
(  9,200)( 10,199)( 11,198)( 12,197)( 13,196)( 14,195)( 15,194)( 16,193)
( 17,192)( 18,191)( 19,190)( 20,189)( 21,188)( 22,187)( 23,186)( 24,185)
( 25,184)( 26,183)( 27,182)( 28,181)( 29,180)( 30,179)( 31,178)( 32,177)
( 33,176)( 34,175)( 35,174)( 36,173)( 37,172)( 38,171)( 39,170)( 40,169)
( 41,168)( 42,167)( 43,166)( 44,165)( 45,164)( 46,163)( 47,162)( 48,161)
( 49,160)( 50,159)( 51,158)( 52,157)( 53,156)( 54,155)( 55,154)( 56,153)
( 57,152)( 58,151)( 59,150)( 60,149)( 61,148)( 62,147)( 63,146)( 64,145)
( 65,144)( 66,143)( 67,142)( 68,141)( 69,140)( 70,139)( 71,138)( 72,137)
( 73,136)( 74,135)( 75,134)( 76,133)( 77,132)( 78,131)( 79,130)( 80,129)
( 81,128)( 82,127)( 83,126)( 84,125)( 85,124)( 86,123)( 87,122)( 88,121)
( 89,120)( 90,119)( 91,118)( 92,117)( 93,116)( 94,115)( 95,114)( 96,113)
( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106);;
s2 := (207,208);;
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*s2*s0*s2, s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(208)!(  2,103)(  3,102)(  4,101)(  5,100)(  6, 99)(  7, 98)(  8, 97)
(  9, 96)( 10, 95)( 11, 94)( 12, 93)( 13, 92)( 14, 91)( 15, 90)( 16, 89)
( 17, 88)( 18, 87)( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 81)
( 25, 80)( 26, 79)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 74)( 32, 73)
( 33, 72)( 34, 71)( 35, 70)( 36, 69)( 37, 68)( 38, 67)( 39, 66)( 40, 65)
( 41, 64)( 42, 63)( 43, 62)( 44, 61)( 45, 60)( 46, 59)( 47, 58)( 48, 57)
( 49, 56)( 50, 55)( 51, 54)( 52, 53)(105,206)(106,205)(107,204)(108,203)
(109,202)(110,201)(111,200)(112,199)(113,198)(114,197)(115,196)(116,195)
(117,194)(118,193)(119,192)(120,191)(121,190)(122,189)(123,188)(124,187)
(125,186)(126,185)(127,184)(128,183)(129,182)(130,181)(131,180)(132,179)
(133,178)(134,177)(135,176)(136,175)(137,174)(138,173)(139,172)(140,171)
(141,170)(142,169)(143,168)(144,167)(145,166)(146,165)(147,164)(148,163)
(149,162)(150,161)(151,160)(152,159)(153,158)(154,157)(155,156);
s1 := Sym(208)!(  1,105)(  2,104)(  3,206)(  4,205)(  5,204)(  6,203)(  7,202)
(  8,201)(  9,200)( 10,199)( 11,198)( 12,197)( 13,196)( 14,195)( 15,194)
( 16,193)( 17,192)( 18,191)( 19,190)( 20,189)( 21,188)( 22,187)( 23,186)
( 24,185)( 25,184)( 26,183)( 27,182)( 28,181)( 29,180)( 30,179)( 31,178)
( 32,177)( 33,176)( 34,175)( 35,174)( 36,173)( 37,172)( 38,171)( 39,170)
( 40,169)( 41,168)( 42,167)( 43,166)( 44,165)( 45,164)( 46,163)( 47,162)
( 48,161)( 49,160)( 50,159)( 51,158)( 52,157)( 53,156)( 54,155)( 55,154)
( 56,153)( 57,152)( 58,151)( 59,150)( 60,149)( 61,148)( 62,147)( 63,146)
( 64,145)( 65,144)( 66,143)( 67,142)( 68,141)( 69,140)( 70,139)( 71,138)
( 72,137)( 73,136)( 74,135)( 75,134)( 76,133)( 77,132)( 78,131)( 79,130)
( 80,129)( 81,128)( 82,127)( 83,126)( 84,125)( 85,124)( 86,123)( 87,122)
( 88,121)( 89,120)( 90,119)( 91,118)( 92,117)( 93,116)( 94,115)( 95,114)
( 96,113)( 97,112)( 98,111)( 99,110)(100,109)(101,108)(102,107)(103,106);
s2 := Sym(208)!(207,208);
poly := sub<Sym(208)|s0,s1,s2>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope