Polytope of Type {5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5}*10
Also Known As : pentagon, {5}. if this polytope has another name.
Group : SmallGroup(10,1)
Rank : 2
Schlafli Type : {5}
Number of vertices, edges, etc : 5, 5
Order of s0s1 : 5
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2} of size 20
   {5,3} of size 60
   {5,5} of size 60
   {5,10} of size 100
   {5,4} of size 120
   {5,6} of size 120
   {5,3} of size 120
   {5,5} of size 120
   {5,6} of size 120
   {5,6} of size 120
   {5,10} of size 120
   {5,10} of size 120
   {5,4} of size 160
   {5,5} of size 160
   {5,4} of size 240
   {5,6} of size 240
   {5,6} of size 240
   {5,10} of size 240
   {5,5} of size 320
   {5,8} of size 320
   {5,8} of size 320
   {5,10} of size 320
   {5,4} of size 320
   {5,10} of size 320
   {5,6} of size 480
   {5,8} of size 480
   {5,12} of size 480
   {5,20} of size 480
   {5,10} of size 500
   {5,5} of size 600
   {5,6} of size 600
   {5,10} of size 600
   {5,15} of size 600
   {5,8} of size 640
   {5,10} of size 640
   {5,4} of size 640
   {5,8} of size 640
   {5,20} of size 640
   {5,20} of size 640
   {5,5} of size 660
   {5,6} of size 660
   {5,6} of size 720
   {5,4} of size 720
   {5,5} of size 720
   {5,8} of size 720
   {5,8} of size 720
   {5,10} of size 720
   {5,5} of size 960
   {5,6} of size 960
   {5,4} of size 1200
   {5,6} of size 1200
   {5,20} of size 1200
   {5,30} of size 1200
   {5,6} of size 1200
   {5,10} of size 1200
   {5,10} of size 1200
   {5,30} of size 1200
   {5,8} of size 1280
   {5,20} of size 1280
   {5,4} of size 1320
   {5,4} of size 1320
   {5,5} of size 1320
   {5,6} of size 1320
   {5,10} of size 1320
   {5,10} of size 1320
   {5,11} of size 1320
   {5,11} of size 1320
   {5,12} of size 1320
   {5,12} of size 1320
   {5,12} of size 1320
   {5,12} of size 1320
   {5,5} of size 1320
   {5,6} of size 1320
   {5,6} of size 1320
   {5,6} of size 1320
   {5,10} of size 1320
   {5,10} of size 1320
   {5,6} of size 1440
   {5,4} of size 1440
   {5,8} of size 1440
   {5,8} of size 1440
   {5,10} of size 1440
   {5,10} of size 1440
   {5,10} of size 1600
   {5,20} of size 1600
   {5,6} of size 1620
   {5,10} of size 1620
   {5,4} of size 1920
   {5,6} of size 1920
   {5,8} of size 1920
   {5,8} of size 1920
   {5,12} of size 1920
   {5,12} of size 1920
   {5,5} of size 1920
   {5,6} of size 1920
   {5,6} of size 1920
   {5,6} of size 1920
   {5,10} of size 1920
   {5,10} of size 1920
   {5,5} of size 1920
   {5,5} of size 1920
   {5,10} of size 1920
   {5,10} of size 1920
   {5,12} of size 1920
   {5,12} of size 1920
   {5,12} of size 1920
   {5,12} of size 1920
Vertex Figure Of :
   {2,5} of size 20
   {3,5} of size 60
   {5,5} of size 60
   {10,5} of size 100
   {4,5} of size 120
   {6,5} of size 120
   {3,5} of size 120
   {5,5} of size 120
   {6,5} of size 120
   {6,5} of size 120
   {10,5} of size 120
   {10,5} of size 120
   {4,5} of size 160
   {5,5} of size 160
   {4,5} of size 240
   {6,5} of size 240
   {6,5} of size 240
   {10,5} of size 240
   {5,5} of size 320
   {8,5} of size 320
   {8,5} of size 320
   {10,5} of size 320
   {4,5} of size 320
   {10,5} of size 320
   {6,5} of size 480
   {8,5} of size 480
   {12,5} of size 480
   {20,5} of size 480
   {10,5} of size 500
   {5,5} of size 600
   {6,5} of size 600
   {10,5} of size 600
   {15,5} of size 600
   {8,5} of size 640
   {10,5} of size 640
   {4,5} of size 640
   {8,5} of size 640
   {20,5} of size 640
   {20,5} of size 640
   {5,5} of size 660
   {6,5} of size 660
   {6,5} of size 720
   {4,5} of size 720
   {5,5} of size 720
   {8,5} of size 720
   {8,5} of size 720
   {10,5} of size 720
   {5,5} of size 960
   {6,5} of size 960
   {4,5} of size 1200
   {6,5} of size 1200
   {20,5} of size 1200
   {30,5} of size 1200
   {6,5} of size 1200
   {10,5} of size 1200
   {10,5} of size 1200
   {30,5} of size 1200
   {8,5} of size 1280
   {20,5} of size 1280
   {4,5} of size 1320
   {4,5} of size 1320
   {5,5} of size 1320
   {6,5} of size 1320
   {10,5} of size 1320
   {10,5} of size 1320
   {11,5} of size 1320
   {11,5} of size 1320
   {12,5} of size 1320
   {12,5} of size 1320
   {12,5} of size 1320
   {12,5} of size 1320
   {5,5} of size 1320
   {6,5} of size 1320
   {6,5} of size 1320
   {6,5} of size 1320
   {10,5} of size 1320
   {10,5} of size 1320
   {6,5} of size 1440
   {4,5} of size 1440
   {8,5} of size 1440
   {8,5} of size 1440
   {10,5} of size 1440
   {10,5} of size 1440
   {10,5} of size 1600
   {20,5} of size 1600
   {6,5} of size 1620
   {10,5} of size 1620
   {4,5} of size 1920
   {6,5} of size 1920
   {8,5} of size 1920
   {8,5} of size 1920
   {12,5} of size 1920
   {12,5} of size 1920
   {5,5} of size 1920
   {6,5} of size 1920
   {6,5} of size 1920
   {6,5} of size 1920
   {10,5} of size 1920
   {10,5} of size 1920
   {5,5} of size 1920
   {5,5} of size 1920
   {10,5} of size 1920
   {10,5} of size 1920
   {12,5} of size 1920
   {12,5} of size 1920
   {12,5} of size 1920
   {12,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10}*20
   3-fold covers : {15}*30
   4-fold covers : {20}*40
   5-fold covers : {25}*50
   6-fold covers : {30}*60
   7-fold covers : {35}*70
   8-fold covers : {40}*80
   9-fold covers : {45}*90
   10-fold covers : {50}*100
   11-fold covers : {55}*110
   12-fold covers : {60}*120
   13-fold covers : {65}*130
   14-fold covers : {70}*140
   15-fold covers : {75}*150
   16-fold covers : {80}*160
   17-fold covers : {85}*170
   18-fold covers : {90}*180
   19-fold covers : {95}*190
   20-fold covers : {100}*200
   21-fold covers : {105}*210
   22-fold covers : {110}*220
   23-fold covers : {115}*230
   24-fold covers : {120}*240
   25-fold covers : {125}*250
   26-fold covers : {130}*260
   27-fold covers : {135}*270
   28-fold covers : {140}*280
   29-fold covers : {145}*290
   30-fold covers : {150}*300
   31-fold covers : {155}*310
   32-fold covers : {160}*320
   33-fold covers : {165}*330
   34-fold covers : {170}*340
   35-fold covers : {175}*350
   36-fold covers : {180}*360
   37-fold covers : {185}*370
   38-fold covers : {190}*380
   39-fold covers : {195}*390
   40-fold covers : {200}*400
   41-fold covers : {205}*410
   42-fold covers : {210}*420
   43-fold covers : {215}*430
   44-fold covers : {220}*440
   45-fold covers : {225}*450
   46-fold covers : {230}*460
   47-fold covers : {235}*470
   48-fold covers : {240}*480
   49-fold covers : {245}*490
   50-fold covers : {250}*500
   51-fold covers : {255}*510
   52-fold covers : {260}*520
   53-fold covers : {265}*530
   54-fold covers : {270}*540
   55-fold covers : {275}*550
   56-fold covers : {280}*560
   57-fold covers : {285}*570
   58-fold covers : {290}*580
   59-fold covers : {295}*590
   60-fold covers : {300}*600
   61-fold covers : {305}*610
   62-fold covers : {310}*620
   63-fold covers : {315}*630
   64-fold covers : {320}*640
   65-fold covers : {325}*650
   66-fold covers : {330}*660
   67-fold covers : {335}*670
   68-fold covers : {340}*680
   69-fold covers : {345}*690
   70-fold covers : {350}*700
   71-fold covers : {355}*710
   72-fold covers : {360}*720
   73-fold covers : {365}*730
   74-fold covers : {370}*740
   75-fold covers : {375}*750
   76-fold covers : {380}*760
   77-fold covers : {385}*770
   78-fold covers : {390}*780
   79-fold covers : {395}*790
   80-fold covers : {400}*800
   81-fold covers : {405}*810
   82-fold covers : {410}*820
   83-fold covers : {415}*830
   84-fold covers : {420}*840
   85-fold covers : {425}*850
   86-fold covers : {430}*860
   87-fold covers : {435}*870
   88-fold covers : {440}*880
   89-fold covers : {445}*890
   90-fold covers : {450}*900
   91-fold covers : {455}*910
   92-fold covers : {460}*920
   93-fold covers : {465}*930
   94-fold covers : {470}*940
   95-fold covers : {475}*950
   96-fold covers : {480}*960
   97-fold covers : {485}*970
   98-fold covers : {490}*980
   99-fold covers : {495}*990
   100-fold covers : {500}*1000
   101-fold covers : {505}*1010
   102-fold covers : {510}*1020
   103-fold covers : {515}*1030
   104-fold covers : {520}*1040
   105-fold covers : {525}*1050
   106-fold covers : {530}*1060
   107-fold covers : {535}*1070
   108-fold covers : {540}*1080
   109-fold covers : {545}*1090
   110-fold covers : {550}*1100
   111-fold covers : {555}*1110
   112-fold covers : {560}*1120
   113-fold covers : {565}*1130
   114-fold covers : {570}*1140
   115-fold covers : {575}*1150
   116-fold covers : {580}*1160
   117-fold covers : {585}*1170
   118-fold covers : {590}*1180
   119-fold covers : {595}*1190
   120-fold covers : {600}*1200
   121-fold covers : {605}*1210
   122-fold covers : {610}*1220
   123-fold covers : {615}*1230
   124-fold covers : {620}*1240
   125-fold covers : {625}*1250
   126-fold covers : {630}*1260
   127-fold covers : {635}*1270
   128-fold covers : {640}*1280
   129-fold covers : {645}*1290
   130-fold covers : {650}*1300
   131-fold covers : {655}*1310
   132-fold covers : {660}*1320
   133-fold covers : {665}*1330
   134-fold covers : {670}*1340
   135-fold covers : {675}*1350
   136-fold covers : {680}*1360
   137-fold covers : {685}*1370
   138-fold covers : {690}*1380
   139-fold covers : {695}*1390
   140-fold covers : {700}*1400
   141-fold covers : {705}*1410
   142-fold covers : {710}*1420
   143-fold covers : {715}*1430
   144-fold covers : {720}*1440
   145-fold covers : {725}*1450
   146-fold covers : {730}*1460
   147-fold covers : {735}*1470
   148-fold covers : {740}*1480
   149-fold covers : {745}*1490
   150-fold covers : {750}*1500
   151-fold covers : {755}*1510
   152-fold covers : {760}*1520
   153-fold covers : {765}*1530
   154-fold covers : {770}*1540
   155-fold covers : {775}*1550
   156-fold covers : {780}*1560
   157-fold covers : {785}*1570
   158-fold covers : {790}*1580
   159-fold covers : {795}*1590
   160-fold covers : {800}*1600
   161-fold covers : {805}*1610
   162-fold covers : {810}*1620
   163-fold covers : {815}*1630
   164-fold covers : {820}*1640
   165-fold covers : {825}*1650
   166-fold covers : {830}*1660
   167-fold covers : {835}*1670
   168-fold covers : {840}*1680
   169-fold covers : {845}*1690
   170-fold covers : {850}*1700
   171-fold covers : {855}*1710
   172-fold covers : {860}*1720
   173-fold covers : {865}*1730
   174-fold covers : {870}*1740
   175-fold covers : {875}*1750
   176-fold covers : {880}*1760
   177-fold covers : {885}*1770
   178-fold covers : {890}*1780
   179-fold covers : {895}*1790
   180-fold covers : {900}*1800
   181-fold covers : {905}*1810
   182-fold covers : {910}*1820
   183-fold covers : {915}*1830
   184-fold covers : {920}*1840
   185-fold covers : {925}*1850
   186-fold covers : {930}*1860
   187-fold covers : {935}*1870
   188-fold covers : {940}*1880
   189-fold covers : {945}*1890
   190-fold covers : {950}*1900
   191-fold covers : {955}*1910
   192-fold covers : {960}*1920
   193-fold covers : {965}*1930
   194-fold covers : {970}*1940
   195-fold covers : {975}*1950
   196-fold covers : {980}*1960
   197-fold covers : {985}*1970
   198-fold covers : {990}*1980
   199-fold covers : {995}*1990
   200-fold covers : {1000}*2000
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(5)!(2,3)(4,5);
s1 := Sym(5)!(1,2)(3,4);
poly := sub<Sym(5)|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 >; 
 
References : None.
to this polytope