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