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# Polytope of Type {320}

Atlas Canonical Name : {320}*640
Also Known As : 320-gon, {320}. if this polytope has another name.
Group : SmallGroup(640,6)
Rank : 2
Schlafli Type : {320}
Number of vertices, edges, etc : 320, 320
Order of s0s1 : 320
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{320,2} of size 1280
Vertex Figure Of :
{2,320} of size 1280
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {160}*320
4-fold quotients : {80}*160
5-fold quotients : {64}*128
8-fold quotients : {40}*80
10-fold quotients : {32}*64
16-fold quotients : {20}*40
20-fold quotients : {16}*32
32-fold quotients : {10}*20
40-fold quotients : {8}*16
64-fold quotients : {5}*10
80-fold quotients : {4}*8
160-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {640}*1280
3-fold covers : {960}*1920
Permutation Representation (GAP) :
```s0 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 11, 16)( 12, 20)( 13, 19)( 14, 18)
( 15, 17)( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)( 27, 40)
( 28, 39)( 29, 38)( 30, 37)( 41, 61)( 42, 65)( 43, 64)( 44, 63)( 45, 62)
( 46, 66)( 47, 70)( 48, 69)( 49, 68)( 50, 67)( 51, 76)( 52, 80)( 53, 79)
( 54, 78)( 55, 77)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 81,121)
( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)( 88,129)( 89,128)
( 90,127)( 91,136)( 92,140)( 93,139)( 94,138)( 95,137)( 96,131)( 97,135)
( 98,134)( 99,133)(100,132)(101,151)(102,155)(103,154)(104,153)(105,152)
(106,156)(107,160)(108,159)(109,158)(110,157)(111,141)(112,145)(113,144)
(114,143)(115,142)(116,146)(117,150)(118,149)(119,148)(120,147)(161,241)
(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)(168,249)(169,248)
(170,247)(171,256)(172,260)(173,259)(174,258)(175,257)(176,251)(177,255)
(178,254)(179,253)(180,252)(181,271)(182,275)(183,274)(184,273)(185,272)
(186,276)(187,280)(188,279)(189,278)(190,277)(191,261)(192,265)(193,264)
(194,263)(195,262)(196,266)(197,270)(198,269)(199,268)(200,267)(201,301)
(202,305)(203,304)(204,303)(205,302)(206,306)(207,310)(208,309)(209,308)
(210,307)(211,316)(212,320)(213,319)(214,318)(215,317)(216,311)(217,315)
(218,314)(219,313)(220,312)(221,281)(222,285)(223,284)(224,283)(225,282)
(226,286)(227,290)(228,289)(229,288)(230,287)(231,296)(232,300)(233,299)
(234,298)(235,297)(236,291)(237,295)(238,294)(239,293)(240,292);;
s1 := (  1,162)(  2,161)(  3,165)(  4,164)(  5,163)(  6,167)(  7,166)(  8,170)
(  9,169)( 10,168)( 11,177)( 12,176)( 13,180)( 14,179)( 15,178)( 16,172)
( 17,171)( 18,175)( 19,174)( 20,173)( 21,192)( 22,191)( 23,195)( 24,194)
( 25,193)( 26,197)( 27,196)( 28,200)( 29,199)( 30,198)( 31,182)( 32,181)
( 33,185)( 34,184)( 35,183)( 36,187)( 37,186)( 38,190)( 39,189)( 40,188)
( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,227)( 47,226)( 48,230)
( 49,229)( 50,228)( 51,237)( 52,236)( 53,240)( 54,239)( 55,238)( 56,232)
( 57,231)( 58,235)( 59,234)( 60,233)( 61,202)( 62,201)( 63,205)( 64,204)
( 65,203)( 66,207)( 67,206)( 68,210)( 69,209)( 70,208)( 71,217)( 72,216)
( 73,220)( 74,219)( 75,218)( 76,212)( 77,211)( 78,215)( 79,214)( 80,213)
( 81,282)( 82,281)( 83,285)( 84,284)( 85,283)( 86,287)( 87,286)( 88,290)
( 89,289)( 90,288)( 91,297)( 92,296)( 93,300)( 94,299)( 95,298)( 96,292)
( 97,291)( 98,295)( 99,294)(100,293)(101,312)(102,311)(103,315)(104,314)
(105,313)(106,317)(107,316)(108,320)(109,319)(110,318)(111,302)(112,301)
(113,305)(114,304)(115,303)(116,307)(117,306)(118,310)(119,309)(120,308)
(121,242)(122,241)(123,245)(124,244)(125,243)(126,247)(127,246)(128,250)
(129,249)(130,248)(131,257)(132,256)(133,260)(134,259)(135,258)(136,252)
(137,251)(138,255)(139,254)(140,253)(141,272)(142,271)(143,275)(144,274)
(145,273)(146,277)(147,276)(148,280)(149,279)(150,278)(151,262)(152,261)
(153,265)(154,264)(155,263)(156,267)(157,266)(158,270)(159,269)(160,268);;
poly := Group([s0,s1]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(320)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 11, 16)( 12, 20)( 13, 19)
( 14, 18)( 15, 17)( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)
( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 41, 61)( 42, 65)( 43, 64)( 44, 63)
( 45, 62)( 46, 66)( 47, 70)( 48, 69)( 49, 68)( 50, 67)( 51, 76)( 52, 80)
( 53, 79)( 54, 78)( 55, 77)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)
( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)( 88,129)
( 89,128)( 90,127)( 91,136)( 92,140)( 93,139)( 94,138)( 95,137)( 96,131)
( 97,135)( 98,134)( 99,133)(100,132)(101,151)(102,155)(103,154)(104,153)
(105,152)(106,156)(107,160)(108,159)(109,158)(110,157)(111,141)(112,145)
(113,144)(114,143)(115,142)(116,146)(117,150)(118,149)(119,148)(120,147)
(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)(168,249)
(169,248)(170,247)(171,256)(172,260)(173,259)(174,258)(175,257)(176,251)
(177,255)(178,254)(179,253)(180,252)(181,271)(182,275)(183,274)(184,273)
(185,272)(186,276)(187,280)(188,279)(189,278)(190,277)(191,261)(192,265)
(193,264)(194,263)(195,262)(196,266)(197,270)(198,269)(199,268)(200,267)
(201,301)(202,305)(203,304)(204,303)(205,302)(206,306)(207,310)(208,309)
(209,308)(210,307)(211,316)(212,320)(213,319)(214,318)(215,317)(216,311)
(217,315)(218,314)(219,313)(220,312)(221,281)(222,285)(223,284)(224,283)
(225,282)(226,286)(227,290)(228,289)(229,288)(230,287)(231,296)(232,300)
(233,299)(234,298)(235,297)(236,291)(237,295)(238,294)(239,293)(240,292);
s1 := Sym(320)!(  1,162)(  2,161)(  3,165)(  4,164)(  5,163)(  6,167)(  7,166)
(  8,170)(  9,169)( 10,168)( 11,177)( 12,176)( 13,180)( 14,179)( 15,178)
( 16,172)( 17,171)( 18,175)( 19,174)( 20,173)( 21,192)( 22,191)( 23,195)
( 24,194)( 25,193)( 26,197)( 27,196)( 28,200)( 29,199)( 30,198)( 31,182)
( 32,181)( 33,185)( 34,184)( 35,183)( 36,187)( 37,186)( 38,190)( 39,189)
( 40,188)( 41,222)( 42,221)( 43,225)( 44,224)( 45,223)( 46,227)( 47,226)
( 48,230)( 49,229)( 50,228)( 51,237)( 52,236)( 53,240)( 54,239)( 55,238)
( 56,232)( 57,231)( 58,235)( 59,234)( 60,233)( 61,202)( 62,201)( 63,205)
( 64,204)( 65,203)( 66,207)( 67,206)( 68,210)( 69,209)( 70,208)( 71,217)
( 72,216)( 73,220)( 74,219)( 75,218)( 76,212)( 77,211)( 78,215)( 79,214)
( 80,213)( 81,282)( 82,281)( 83,285)( 84,284)( 85,283)( 86,287)( 87,286)
( 88,290)( 89,289)( 90,288)( 91,297)( 92,296)( 93,300)( 94,299)( 95,298)
( 96,292)( 97,291)( 98,295)( 99,294)(100,293)(101,312)(102,311)(103,315)
(104,314)(105,313)(106,317)(107,316)(108,320)(109,319)(110,318)(111,302)
(112,301)(113,305)(114,304)(115,303)(116,307)(117,306)(118,310)(119,309)
(120,308)(121,242)(122,241)(123,245)(124,244)(125,243)(126,247)(127,246)
(128,250)(129,249)(130,248)(131,257)(132,256)(133,260)(134,259)(135,258)
(136,252)(137,251)(138,255)(139,254)(140,253)(141,272)(142,271)(143,275)
(144,274)(145,273)(146,277)(147,276)(148,280)(149,279)(150,278)(151,262)
(152,261)(153,265)(154,264)(155,263)(156,267)(157,266)(158,270)(159,269)
(160,268);
poly := sub<Sym(320)|s0,s1>;

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

```
References : None.
to this polytope