User:Tomruen/List of uniform polyhedra and tilings

See: User:Tomruen/polyhedron db testing

Convex regulars

edit
Tetrahedron
{{{T-name2}}}
Self-dual
{{{T-dual2}}}
U01 T:Tet
3 | 2 3
| 2 2 2

      =      
     
     

3.3.3
4{3}
F=4
E=6
V=4
Td, A3, [3,3], (*332) W1
K06
C15
       
Octahedron
{{{O-name2}}}
Cube
{{{O-dual2}}}
U05 O:Oct
4 | 2 3

     

3.3.3.3
8{3}
F=8
E=12
V=6
Oh, BC3, [4,3], (*432) W2
K10
C17
       
Hexahedron
{{{C-name2}}}
Octahedron
{{{C-dual2}}}
U06 C:Cube
3 | 2 4

     

4.4.4
6{4}
F=6
E=12
V=8
Oh, B3, [4,3], (*432) W3
K11
C18
       
Icosahedron
{{{I-name2}}}
Regular dodecahedron
{{{I-dual2}}}
U22 I:Ike
5 | 2 3

     

3.3.3.3.3
20{3}
F=20
E=30
V=12
Ih, H3, [5,3], (*532) W4
K27
C25
       
Dodecahedron
{{{D-name2}}}
Regular icosahedron
{{{D-dual2}}}
U23 D:Doe
3 | 2 5

     

5.5.5
12{5}
F=12
E=30
V=20
Ih, H3, [5,3], (*532) W5
K28
C26
       

Nonconvex regulars

edit
Great dodecahedron
{{{gD-name2}}}
Small stellated dodecahedron
{{{gD-dual2}}}
U35 gD:Gad
52 | 2 5

       

(55)/2
12{5}
F=12
E=30
V=12
Ih, H3, [5,3], (*532) W21
K40
C44
    [[Image:{{{gD-netimage}}}|50px]]  
Small stellated dodecahedron
{{{lsD-name2}}}
Great dodecahedron
{{{lsD-dual2}}}
U34 lsD:Sissid
5 | 2 52

       

(52)5
12 5
F=12
E=30
V=12
Ih, H3, [5,3], (*532) W20
K39
C43
    [[Image:{{{lsD-netimage}}}|50px]]  
Great icosahedron
{{{gI-name2}}}
Great stellated dodecahedron
{{{gI-dual2}}}
U53 gI:Gike
52 | 2 3

       

(35)/2
20{3}
F=20
E=30
V=12
Ih, H3, [5,3], (*532) W41
K58
C69
    [[Image:{{{gI-netimage}}}|50px]]  
Great stellated dodecahedron
{{{gsD-name2}}}
Great icosahedron
{{{gsD-dual2}}}
U52 gsD:Gissid
3 | 2 52

       

(52)3
12 { 52 }
F=12
E=30
V=20
Ih, H3, [5,3], (*532) W22
K57
C68
    [[Image:{{{gsD-netimage}}}|50px]]  

Semiregulars

edit
Truncated tetrahedron
{{{tT-name2}}}
Triakis tetrahedron
{{{tT-dual2}}}
U02 tT:Tut
2 3 | 3

      =      

3.6.6
4{3}+4{6}
F=8
E=18
V=12
Td, A3, [3,3], (*332), order 24 W6
K07
C16
       
Truncated octahedron
{{{tO-name2}}}
Tetrakis hexahedron
{{{tO-dual2}}}
U08 tO:Toe
2 4 | 3
3 3 2 |

     
     

4.6.6
6{4}+8{6}
F=14
E=36
V=24
Oh, B3, [4,3], (*432), order 48
Th, [3,3] and (*332), order 24
W7
K13
C20
       
Truncated cube
{{{tC-name2}}}
Triakis octahedron
{{{tC-dual2}}}
U09 tC:Tic
2 3 | 4

     

3.8.8
8{3}+6{8}
F=14
E=36
V=24
Oh, B3, [4,3], (*432), order 48 W8
K14
C21
       
Truncated icosahedron
{{{tI-name2}}}
Pentakis dodecahedron
{{{tI-dual2}}}
U25 tI:Ti
2 5 | 3

     

5.6.6
12{5}+20{6}
F=32
E=90
V=60
Ih, H3, [5,3], (*532), order 120 W9
K30
C27
       
Truncated dodecahedron
{{{tD-name2}}}
Triakis icosahedron
{{{tD-dual2}}}
U26 tD:Tid
2 3 | 5

     

3.10.10
20{3}+12{10}
F=32
E=90
V=60
Ih, H3, [5,3], (*532), order 120 W10
K31
C29
       
Cuboctahedron
{{{CO-name2}}}
Rhombic dodecahedron
{{{CO-dual2}}}
U07 CO:Co
2 | 3 4
3 3 | 2

      or    
      or    

3.4.3.4
8{3}+6{4}
F=14
E=24
V=12
Oh, B3, [4,3], (*432), order 48
Td, [3,3], (*332), order 24
W11
K12
C19
       
Icosidodecahedron
{{{ID-name2}}}
Rhombic triacontahedron
{{{ID-dual2}}}
U24 ID:Id
2 | 3 5

     

3.5.3.5
20{3}+12{5}
F=32
E=60
V=30
Ih, H3, [5,3], (*532), order 120 W12
K29
C28
       
Rhombicuboctahedron
{{{lrCO-name2}}}
Deltoidal icositetrahedron
{{{lrCO-dual2}}}
U10 lrCO:Sirco
3 4 | 2

     

3.4.4.4
8{3}+(6+12){4}
F=26
E=48
V=24
Oh, B3, [4,3], (*432), order 48 W13
K15
C22
       
Rhombicosidodecahedron
{{{lrID-name2}}}
Deltoidal hexecontahedron
{{{lrID-dual2}}}
U27 lrID:Srid
3 5 | 2

     

3.4.5.4
20{3}+30{4}+12{5}
F=62
E=120
V=60
Ih, H3, [5,3], (*532), order 120 W14
K32
C30
       
Truncated cuboctahedron
{{{grCO-name2}}}
Disdyakis dodecahedron
{{{grCO-dual2}}}
U11 grCO:Girco
2 3 4 |

     

4.6.8
12{4}+8{6}+6{8}
F=26
E=72
V=48
Oh, B3, [4,3], (*432), order 48 W15
K16
C23
       
Truncated icosidodecahedron
{{{grID-name2}}}
Disdyakis triacontahedron
{{{grID-dual2}}}
U28 grID:Grid
2 3 5 |

     

4.6.10
30{4}+20{6}+12{10}
F=62
E=180
V=120
Ih, H3, [5,3], (*532), order 120 W16
K33
C31
       
Snub cube
{{{nCO-name2}}}
Pentagonal icositetrahedron
{{{nCO-dual2}}}
U12 nCO:Snic
| 2 3 4

     

3.3.3.3.4
(8+24){3}+6{4}
F=38
E=60
V=24
O, 1/2B3, [4,3]+, (432), order 24 W17
K17
C24
       
Snub dodecahedron
{{{nID-name2}}}
Pentagonal hexecontahedron
{{{nID-dual2}}}
U29 nID:Snid
| 2 3 5

     

3.3.3.3.5
(20+60){3}+12{5}
F=92
E=150
V=60
I, 1/2H3, [5,3]+, (532), order 60 W18
K34
C32
       

Semiregular duals

edit
Triakis tetrahedron F=12
E=18
V=8
Td, A3, [3,3], (*332)       Dual:Truncated tetrahedron
Tetrakis hexahedron F=24
E=36
V=14
Oh, B3, [4,3], (*432)       Dual:Truncated octahedron
Triakis octahedron F=24
E=36
V=14
Oh, B3, [4,3], (*432)       Dual:Truncated cube
Pentakis dodecahedron F=60
E=90
V=32
Ih, H3, [5,3], (*532)       Dual:Truncated icosahedron
Triakis icosahedron F=60
E=90
V=32
Ih, H3, [5,3], (*532)       Dual:Truncated dodecahedron
Rhombic dodecahedron F=12
E=24
V=14
Oh, B3, [4,3], (*432)       Dual:Cuboctahedron
Rhombic triacontahedron F=30
E=60
V=32
Ih, H3, [5,3], (*532) File:Rhombictriacontahedron.png     Dual:Icosidodecahedron

Incomplete

[[{{{dlrCO-name}}}]] F={{{dlrCO-F}}}
E={{{dlrCO-E}}}
V={{{dlrCO-V}}}
{{{dlrCO-group}}} [[Image:{{{dlrCO-image}}}|50px]] [[Image:{{{dlrCO-netimage}}}|50px]] [[Image:{{{dlrCO-dimage}}}|50px]] Dual:[[{{{dlrCO-dual}}}]]
[[{{{dlrID-name}}}]] F={{{dlrID-F}}}
E={{{dlrID-E}}}
V={{{dlrID-V}}}
{{{dlrID-group}}} [[Image:{{{dlrID-image}}}|50px]] [[Image:{{{dlrID-netimage}}}|50px]] [[Image:{{{dlrID-dimage}}}|50px]] Dual:[[{{{dlrID-dual}}}]]
[[{{{dgrCO-name}}}]] F={{{dgrCO-F}}}
E={{{dgrCO-E}}}
V={{{dgrCO-V}}}
{{{dgrCO-group}}} [[Image:{{{dgrCO-image}}}|50px]] [[Image:{{{dgrCO-netimage}}}|50px]] [[Image:{{{dgrCO-dimage}}}|50px]] Dual:[[{{{dgrCO-dual}}}]]
[[{{{dgrID-name}}}]] F={{{dgrID-F}}}
E={{{dgrID-E}}}
V={{{dgrID-V}}}
{{{dgrID-group}}} [[Image:{{{dgrID-image}}}|50px]] [[Image:{{{dgrID-netimage}}}|50px]] [[Image:{{{dgrID-dimage}}}|50px]] Dual:[[{{{dgrID-dual}}}]]
[[{{{dnCO-name}}}]] F={{{dnCO-F}}}
E={{{dnCO-E}}}
V={{{dnCO-V}}}
{{{dnCO-group}}} [[Image:{{{dnCO-image}}}|50px]] [[Image:{{{dnCO-netimage}}}|50px]] [[Image:{{{dnCO-dimage}}}|50px]] Dual:[[{{{dnCO-dual}}}]]
[[{{{dnID-name}}}]] F={{{dnID-F}}}
E={{{dnID-E}}}
V={{{dnID-V}}}
{{{dnID-group}}} [[Image:{{{dnID-image}}}|50px]] [[Image:{{{dnID-netimage}}}|50px]] [[Image:{{{dnID-dimage}}}|50px]] Dual:[[{{{dnID-dual}}}]]

Nonconvex

edit
Octahemioctahedron
Octahemioctacron
U03 OhO:Oho
3/2 3 | 3

{{{OhO-CD}}}

3.6.3/2.6
8{3}+4{6}
F=12
E=24
V=12
Oh, [4,3], *432 W68
K08
C37
    [[Image:{{{OhO-netimage}}}|50px]]  


Tetrahemihexahedron
Tetrahemihexacron
U04 ThH:Thah
3/2 3 | 2 (double-covering)

{{{ThH-CD}}}

3.4.3/2.4
4{3}+3{4}
F=7
E=12
V=6
Td, [3,3], *332 W67
K09
C36
    [[Image:{{{ThH-netimage}}}|50px]]  


Small cubicuboctahedron
Small hexacronic icositetrahedron
Small sagittal disdodecahedron
U13 lCCO:Socco
3/2 4 | 4
3 4/3 | 4

{{{lCCO-CD}}}

4.8.3/2.8
8{3}+6{4}+6{8}
F=20
E=48
V=24
Oh, [4,3], *432 W69
K18
C38
    [[Image:{{{lCCO-netimage}}}|50px]]  


Great cubicuboctahedron
Great hexacronic icositetrahedron
Great lanceal disdodecahedron
U14 gCCO:Gocco
3 4 | 4/3
4 3/2 | 4

{{{gCCO-CD}}}

3.8/3.4.8/3
8{3}+6{4}+6{8/3}
F=20
E=48
V=24
Oh, [4,3], *432 W77
K19
C50
    [[Image:{{{gCCO-netimage}}}|50px]]  


Cubohemioctahedron
Hexahemioctacron
U15 ChO:Cho
4/3 4 | 3 (double-covering)

{{{ChO-CD}}}

4.6.4/3.6
6{4}+4{6}
F=10
E=24
V=12
Oh, [4,3], *432 W78
K20
C51
    [[Image:{{{ChO-netimage}}}|50px]]  


Cubitruncated cuboctahedron
Tetradyakis hexahedron
Trisdyakis octahedron
U16 ctCO:Cotco
3 4 4/3 |

{{{ctCO-CD}}}

6.8.8/3
8{6}+6{8}+6{8/3}
F=20
E=72
V=48
Oh, [4,3], *432 W79
K21
C52
    [[Image:{{{ctCO-netimage}}}|50px]]  


Nonconvex great rhombicuboctahedron
Great rhombicuboctahedron
Great deltoidal icositetrahedron
Great sagittal disdodecahedron
U17 ugrCO:Querco
3/2 4 | 2
3 4/3 | 2

{{{ugrCO-CD}}}

4.4.4.3/2
8{3}+(6+12){4}
F=26
E=48
V=24
Oh, [4,3], *432 W85
K22
C59
    [[Image:{{{ugrCO-netimage}}}|50px]]  


Small rhombihexahedron
Small rhombicube
Small rhombihexacron
Small dipteral disdodecahedron
U18 lrH:Sroh
2 4 (3/2 4/2) |

{{{lrH-CD}}}

4.8.4/3.8/7
12{4}+6{8}
F=18
E=48
V=24
Oh, [4,3], *432 W86
K23
C60
    [[Image:{{{lrH-netimage}}}|50px]]  


Stellated truncated hexahedron
Stellatruncated cube
Great triakis octahedron
U19 stH:Quith
2 3 | 4/3
2 3/2 | 4/3

{{{stH-CD}}}

3.8/3.8/3
8{3}+6{8/3}
F=14
E=36
V=24
Oh, [4,3], *432 W92
K24
C66
    [[Image:{{{stH-netimage}}}|50px]]  


Great truncated cuboctahedron
Stellatruncated cuboctahedron
Great disdyakis dodecahedron
U20 gtCO:Quitco
2 3 4/3 |

{{{gtCO-CD}}}

4.6/5.8/3
12{4}+8{6}+6{8/3}
F=26
E=72
V=48
Oh, [4,3], *432 W93
K25
C67
    [[Image:{{{gtCO-netimage}}}|50px]]  


Great rhombihexahedron
Great rhombicube
Great rhombihexacron
Great dipteral disdodecahedron
U21 grH:Groh
2 4/3 (3/2 4/2) |

{{{grH-CD}}}

4.8/3.4/3.8/5
12{4}+6{8/3}
F=18
E=48
V=24
Oh, [4,3], *432 W103
K26
C82
    [[Image:{{{grH-netimage}}}|50px]]  


Small ditrigonal icosidodecahedron
Small triambic icosahedron
U30 ldID:Sidtid
3 | 5/2 3

{{{ldID-CD}}}

(3.5/2)3
20{3}+12{5/2}
F=32
E=60
V=20
Ih, [5,3], *532 W70
K35
C39
    [[Image:{{{ldID-netimage}}}|50px]]  


Small icosicosidodecahedron
Small icosified icosidodecahedron
Small icosacronic hexecontahedron
Small lanceal trisicosahedron
U31 lIID:Siid
5/2 3 | 3

{{{lIID-CD}}}

6.5/2.6.3
20{3}+12{5/2}+20{6}
F=52
E=120
V=60
Ih, [5,3], *532 W71
K36
C40
    [[Image:{{{lIID-netimage}}}|50px]]  


Small snub icosicosidodecahedron
Snub disicosidodecahedron
Small hexagonal hexecontahedron
U32 Seside:Seside
| 5/2 3 3

{{{Seside-CD}}}

35.5/2
(40+60){3}+12{5/2}
F=112
E=180
V=60
Ih, [5,3], *532 W110
K37
C41
    [[Image:{{{Seside-netimage}}}|50px]]  


Small dodecicosidodecahedron
Small dodekicosidodecahedron
Small dodecacronic hexecontahedron
Small sagittal ditriacontadron
U33 lDID:Saddid
3/2 5 | 5
3 5/4 | 5

{{{lDID-CD}}}

5.10.3/2.10
20{3}+12{5}+12{10}
F=44
E=120
V=60
Ih, [5,3], *532 W72
K38
C42
    [[Image:{{{lDID-netimage}}}|50px]]  


Dodecadodecahedron
Medial rhombic triacontahedron
U36 DD:Did
2 | 5 5/2
2 | 5 5/3
2 | 5/2 5/4
2 | 5/3 5/4

{{{DD-CD}}}

5.5/2.5.5/2
12{5}+12{5/2}
F=24
E=60
V=30
Ih, [5,3], *532 W73
K41
C45
    [[Image:{{{DD-netimage}}}|50px]]  


Truncated great dodecahedron
Great truncated dodecahedron
Small stellapentakis dodecahedron
Small astropentakis dodecahedron
U37 tgD:Tigid
2 5/2 | 5
2 5/3 | 5

{{{tgD-CD}}}

10.10.5/2
12{5/2}+12{10}
F=24
E=90
V=60
Ih, [5,3], *532 W75
K42
C47
    [[Image:{{{tgD-netimage}}}|50px]]  


Rhombidodecadodecahedron
Medial deltoidal hexecontahedron
Midly lanceal ditriacontahedron
U38 rDD:Raded
5/2 5 | 2

{{{rDD-CD}}}

4.5/2.4.5
30{4}+12{5}+12{5/2}
F=54
E=120
V=60
Ih, [5,3], *532 W76
K43
C48
    [[Image:{{{rDD-netimage}}}|50px]]  


Small rhombidodecahedron
Small rhombidodecacron
Small dipteral ditriacontahedron
U39 lrD:Sird
2 5 (3/2 5/2) |

{{{lrD-CD}}}

4.10.4/3.10/9
30{4}+12{10}
F=42
E=120
V=60
Ih, [5,3], *532 W74
K44
C46
    [[Image:{{{lrD-netimage}}}|50px]]  


Snub dodecadodecahedron
Medial pentagonal hexecontahedron
Midly petaloid ditriacontahedron
U40 Siddid:Siddid
| 2 5/2 5

{{{Siddid-CD}}}

3.3.5/2.3.5
60{3}+12{5}+12{5/2}
F=84
E=150
V=60
I, [5,3]+, 532 W111
K45
C49
    [[Image:{{{Siddid-netimage}}}|50px]]  


Ditrigonal dodecadodecahedron
Medial triambic icosahedron
U41 dDD:Ditdid
3 | 5/3 5
3/2 | 5 5/2
3/2 | 5/3 5/4
3 | 5/2 5/4

{{{dDD-CD}}}

(5.5/3)3
12{5}+12{5/2}
F=24
E=60
V=20
Ih, [5,3], *532 W80
K46
C53
    [[Image:{{{dDD-netimage}}}|50px]]  


Great ditrigonal dodecicosidodecahedron
Great dodekified icosidodecahedron
Great ditrigonal dodecacronic hexecontahedron
Great lanceal trisicosahedron
U42 gdDID:Gidditdid
3 5 | 5/3
5/4 3/2 | 5/3

{{{gdDID-CD}}}

3.10/3.5.10/3
20{3}+12{5}+12{10/3}
F=44
E=120
V=60
Ih, [5,3], *532 W81
K47
C54
    [[Image:{{{gdDID-netimage}}}|50px]]  


Small ditrigonal dodecicosidodecahedron
Small dodekified icosidodecahedron
Small ditrigonal dodecacronic hexecontahedron
Small sagittal trisicosahedron
U43 ldDID:Sidditdid
5/3 3 | 5
5/2 3/2 | 5

{{{ldDID-CD}}}

3.10.5/3.10
20{3}+12{5/2}+12{10}
F=44
E=120
V=60
Ih, [5,3], *532 W82
K48
C55
    [[Image:{{{ldDID-netimage}}}|50px]]  


Icosidodecadodecahedron
Icosified dodecadodecahedron
Medial icosacronic hexecontahedron
Midly sagittal ditriacontahedron
U44 IDD:Ided
5/3 5 | 3
5/2 5/4 | 3

{{{IDD-CD}}}

5.6.5/3.6
12{5}+12{5/2}+20{6}
F=44
E=120
V=60
Ih, [5,3], *532 W83
K49
C56
    [[Image:{{{IDD-netimage}}}|50px]]  


Icositruncated dodecadodecahedron
Tridyakis icosahedron
U45 itDD:Idtid
3 5 5/3 |

{{{itDD-CD}}}

6.10.10/3
20{6}+12{10}+12{10/3}
F=44
E=180
V=120
Ih, [5,3], *532 W84
K50
C57
    [[Image:{{{itDD-netimage}}}|50px]]  


Snub icosidodecadodecahedron
Medial hexagonal hexecontahedron
Petaloidal trisicosahedron
U46 Sided:Sided
| 5/3 3 5

{{{Sided-CD}}}

3.3.3.5.3.5/3
(20+60){3}+12{5}+12{5/2}
F=104
E=180
V=60
I, [5,3]+, 532 W112
K51
C58
    [[Image:{{{Sided-netimage}}}|50px]]  


Great ditrigonal icosidodecahedron
Great triambic icosahedron
U47 gdID:Gidtid
3/2 | 3 5
3 | 3/2 5
3 | 3 5/4
3/2 | 3/2 5/4

{{{gdID-CD}}}

((3.5)3)/2
20{3}+12{5}
F=32
E=60
V=20
Ih, [5,3], *532 W87
K52
C61
    [[Image:{{{gdID-netimage}}}|50px]]  


Great icosicosidodecahedron
Great icosified icosidodecahedron
Great icosacronic hexecontahedron
Great sagittal trisicosahedron
U48 gIID:Giid
3/2 5 | 3
3 5/4 | 3

{{{gIID-CD}}}

5.6.3/2.6
20{3}+12{5}+20{6}
F=52
E=120
V=60
Ih, [5,3], *532 W88
K53
C62
    [[Image:{{{gIID-netimage}}}|50px]]  


Small icosihemidodecahedron
Small icosihemidodecacron
U49 lIhD:Seihid
3/2 3 | 5 (double covering)

{{{lIhD-CD}}}

3.10.3/2.10
20{3}+6{10}
F=26
E=60
V=30
Ih, [5,3], *532 W89
K54
C63
    [[Image:{{{lIhD-netimage}}}|50px]]  


Small dodecicosahedron
Small dodekicosahedron
Small dodecicosacron
Small dipteral trisicosahedron
U50 lDI:Siddy
3 5 (3/2 5/4) |

{{{lDI-CD}}}

6.10.6/5.10/9
20{6}+12{10}
F=32
E=120
V=60
Ih, [5,3], *532 W90
K55
C64
    [[Image:{{{lDI-netimage}}}|50px]]  


Small dodecahemidodecahedron
Small dodecahemidodecacron
U51 lDhD:Sidhid
5/4 5 | 5 (double covering)

{{{lDhD-CD}}}

5.10.5/4.10
12{5}+6{10}
F=18
E=60
V=30
Ih, [5,3], *532 W91
K56
C65
    [[Image:{{{lDhD-netimage}}}|50px]]  


Great icosidodecahedron
Great rhombic triacontahedron
U54 gID:Gid
2 | 3 5/2
2 | 3 5/3
2 | 3/2 5/2
2 | 3/2 5/3

{{{gID-CD}}}

3.5/2.3.5/2
20{3}+12{5/2}
F=32
E=60
V=30
Ih, [5,3], *532 W94
K59
C70
    [[Image:{{{gID-netimage}}}|50px]]  


Truncated great icosahedron
Great truncatedicosahedron
Great stellapentakis dodecahedron
Great astroapentakis dodecahedron
U55 gtI:Tiggy
2 5/2 | 3
2 5/3 | 3

{{{gtI-CD}}}

6.6.5/2
12{5/2}+20{6}
F=32
E=90
V=60
Ih, [5,3], *532 W95
K60
C71
    [[Image:{{{gtI-netimage}}}|50px]]  


Rhombicosahedron
Rhombicosacron
Midly dipteral ditriacontagedron
U56 rI:Ri
2 3 (5/4 5/2) |

{{{rI-CD}}}

4.6.4/3.6/5
30{4}+20{6}
F=50
E=120
V=60
Ih, [5,3], *532 W96
K61
C72
    [[Image:{{{rI-netimage}}}|50px]]  


Great snub icosidodecahedron
Great vertisnub icosadodecahedron
Great pentagonal hexecontahedron
Great dentoid ditriacontahedron
U57 Gosid:Gosid
| 2 5/2 3

{{{Gosid-CD}}}

34.5/2
(20+60){3}+12{5/2}
F=92
E=150
V=60
I, [5,3]+, 532 W113
K62
C88
    [[Image:{{{Gosid-netimage}}}|50px]]  


Small stellated truncated dodecahedron
Small stellatruncated dodecahedron
Great pentakis dodecahedron
U58 lstD:Quit Sissid
2 5 | 5/3
2 5/4 | 5/3

{{{lstD-CD}}}

5.10/3.10/3
12{5}+12{10/3}
F=24
E=90
V=60
Ih, [5,3], *532 W97
K63
C74
    [[Image:{{{lstD-netimage}}}|50px]]  


Truncated dodecadodecahedron
Stellatruncated dodecadodecahedron
Medial disdyakis triacontahedron
Midly disdyakis triacontahedron
U59 tDD:Quitdid
2 5 5/3 |

{{{tDD-CD}}}

4.10/9.10/3
30{4}+12{10}+12{10/3}
F=54
E=180
V=120
Ih, [5,3], *532 W98
K64
C75
    [[Image:{{{tDD-netimage}}}|50px]]  


Inverted snub dodecadodecahedron
Vertisnub dodecadodecahedron
Medial inverted pentagonal hexecontahedron
Medly dentoid ditriacontahedron
U60 Isdid:Isdid
| 5/3 2 5

{{{Isdid-CD}}}

3.3.5.3.5/3
60{3}+12{5}+12{5/2}
F=84
E=150
V=60
I, [5,3]+, 532 W114
K65
C76
    [[Image:{{{Isdid-netimage}}}|50px]]  


Great dodecicosidodecahedron
Great dodekicosidodecahedron
Great dodecacronic hexecontahedron
Great lanceal ditriacontahedron
U61 gDID:Gaddid
5/2 3 | 5/3
5/3 3/2 | 5/3

{{{gDID-CD}}}

3.10/3.5/2.10/7
20{3}+12{5/2}+12{10/3}
F=44
E=120
V=60
Ih, [5,3], *532 W99
K66
C77
    [[Image:{{{gDID-netimage}}}|50px]]  


Small dodecahemicosahedron
Great dodecahemicosahedron
Small dodecahemicosacron
U62 lDhI:Sidhei
5/3 5/2 | 3 (double covering)

{{{lDhI-CD}}}

6.5/2.6.5/3
12{5/2}+10{6}
F=22
E=60
V=30
Ih, [5,3], *532 W100
K67
C78
    [[Image:{{{lDhI-netimage}}}|50px]]  


Great dodecicosahedron
Great dodekicosahedron
Great dodecicosacron
Great dipteral trisicosahedron
U63 gDI:Giddy
3 5/3 (3/2 5/2) |

{{{gDI-CD}}}

6.10/3.6/5.10/7
20{6}+12{10/3}
F=32
E=120
V=60
Ih, [5,3], *532 W101
K68
C79
    [[Image:{{{gDI-netimage}}}|50px]]  


Great snub dodecicosidodecahedron
Great snub dodekicosidodecahedron
Great hexagonal hexecontahedron
U64 Gisdid:Gisdid
| 5/3 5/2 3

{{{Gisdid-CD}}}

3.3.3.5/2.3.5/3
(20+60){3}+(12+12){5/2}
F=104
E=180
V=60
I, [5,3]+, 532 W115
K69
C80
    [[Image:{{{Gisdid-netimage}}}|50px]]  


Great dodecahemicosahedron
Small dodecahemiicosahedron
Great dodecahemicosacron
U65 gDhI:Gidhei
5/4 5 | 3 (double covering)

{{{gDhI-CD}}}

5.6.5/4.6
12{5}+10{6}
F=22
E=60
V=30
Ih, [5,3], *532 W102
K70
C81
    [[Image:{{{gDhI-netimage}}}|50px]]  


Great stellated truncated dodecahedron
Great stellatruncated dodecahedron
Great triakis icosahedron
U66 gstD:Quit Gissid
2 3 | 5/3

{{{gstD-CD}}}

3.10/3.10/3
20{3}+12{10/3}
F=32
E=90
V=60
Ih, [5,3], *532 W104
K71
C83
    [[Image:{{{gstD-netimage}}}|50px]]  


Nonconvex great rhombicosidodecahedron
Great rhombicosidodecahedron
Great deltoidal hexecontahedron
Great sagittal ditriacontahedron
U67 ugrID:Qrid
5/3 3 | 2
5/2 3/2 | 2

{{{ugrID-CD}}}

3.4.5/3.4
20{3}+30{4}+12{5/2}
F=62
E=120
V=60
Ih, [5,3], *532 W105
K72
C84
    [[Image:{{{ugrID-netimage}}}|50px]]  


Great truncated icosidodecahedron
Stellatruncated icosidodecahedron
Great disdyakis triacontahedron
U68 gtID:Gaquatid
2 3 5/3 |

{{{gtID-CD}}}

4.6.10/3
30{4}+20{6}+12{10/3}
F=62
E=180
V=120
Ih, [5,3], *532 W108
K73
C87
    [[Image:{{{gtID-netimage}}}|50px]]  


Great inverted snub icosidodecahedron
Great snub icosidodecahedron
Great inverted pentagonal hexecontahedron
Great petaloid ditriacontahedron
U69 Gisid:Gisid
| 5/3 2 3

{{{Gisid-CD}}}

34.5/3
(20+60){3}+12{5/2}
F=92
E=150
V=60
I, [5,3]+, 532 W116
K74
C73
    [[Image:{{{Gisid-netimage}}}|50px]]  


Great dodecahemidodecahedron
Great dodecahemidodecacron
U70 gDhD:Gidhid
5/3 5/2 | 5/3 (double covering)

{{{gDhD-CD}}}

5/2.10/3.5/3.10/3
12{5/2}+6{10/3}
F=18
E=60
V=30
Ih, [5,3], *532 W107
K75
C86
    [[Image:{{{gDhD-netimage}}}|50px]]  


Great icosihemidodecahedron
Great icosihemidodecacron
U71 gIhD:Geihid
3/2 3 | 5/3

{{{gIhD-CD}}}

3.10/3.3/2.10/3
20{3}+6{10/3}
F=26
E=60
V=30
Ih, [5,3], *532 W106
K76
C85
    [[Image:{{{gIhD-netimage}}}|50px]]  


Small retrosnub icosicosidodecahedron
Retrosnub disicosidodecahedron
Small hexagrammic hexecontahedron
U72 Sirsid:Sirsid
| 3/2 3/2 5/2

{{{Sirsid-CD}}}

(35.5/3)/2
(40+60){3}+12{5/2}
F=112
E=180
V=60
Ih, [5,3], *532 W118
K77
C91
    [[Image:{{{Sirsid-netimage}}}|50px]]  


Great rhombidodecahedron
Great rhombidodecacron
Great dipteral ditriacontahedron
U73 grD:Gird
2 5/3 (3/2 5/4) |

{{{grD-CD}}}

4.10/3.4/3.10/7
30{4}+12{10/3}
F=42
E=120
V=60
Ih, [5,3], *532 W109
K78
C89
    [[Image:{{{grD-netimage}}}|50px]]  


Great retrosnub icosidodecahedron
Great pentagrammic hexecontahedron
Great astroid ditriacontahedron
U74 Girsid:Girsid
| 2 3/2 5/3

{{{Girsid-CD}}}

(34.5/2)/2
(20+60){3}+12{5/2}
F=92
E=150
V=60
I, [5,3]+, 532 W117
K79
C90
    [[Image:{{{Girsid-netimage}}}|50px]]  


Great dirhombicosidodecahedron
Great dirhombicosidodecacron
U75 Gidrid:Gidrid
| 3/2 5/3 3 5/2

{{{Gidrid-CD}}}

4.5/3.4.3.4.5/2.4.3/2
40{3}+60{4}+24{5/2}
F=124
E=240
V=60
Ih, [5,3], *532 W119
K80
C92
    [[Image:{{{Gidrid-netimage}}}|50px]]  


Great disnub dirhombidodecahedron
Great disnub dirhombidodecacron
U- Skilling:Gidisdrid
| (3/2) 5/3 (3) 5/2

{{{Skilling-CD}}}

(5/2.4.3.3.3.4. 5/3.4.3/2.3/2.3/2.4)/2
120{3}+60{4}+24{5/2}
F=204
E=360
V=60
Ih, [5,3], *532 W-
K-
C-
    [[Image:{{{Skilling-netimage}}}|50px]]  


Convex prisms and antiprisms

edit
triangular prism
{{{P3-name2}}}
Triangular dipyramid
{{{P3-dual2}}}
U76(a) P3:Trip
2 3 | 2

     

4.4.3
3{4}+2{3}
F=5
E=9
V=6
D3h, [3,2], (*322), order 12 W--
K01(a)
C--
    [[Image:{{{P3-netimage}}}|50px]]  
Cube
{{{P4-name2}}}
Octahedron
{{{P4-dual2}}}
U76(b) P4:Cube
2 4 | 2
2 2 2 |

     
     
     
     

4.4.4
4{4}+2{4}
F=6
E=12
V=8
D4h, [4,2], (*422), order 16 W--
K01(b)
C--
    [[Image:{{{P4-netimage}}}|50px]]  
pentagonal prism
{{{P5-name2}}}
Pentagonal dipyramid
{{{P5-dual2}}}
U76(c) P5:Pip
2 5 | 2

     

4.4.5
5{4}+2{5}
F=7
E=15
V=10
D5h, [5,2], (*522), order 20 W--
K01(c)
C--
    [[Image:{{{P5-netimage}}}|50px]]  
hexagonal prism
{{{P6-name2}}}
Hexagonal dipyramid
{{{P6-dual2}}}
U76(d) P6:Hip
2 6 | 2
2 2 3 |

     
     
     
     

4.4.6
6{4}+2{6}
F=8
E=18
V=12
D6h, [6,2], (*622), order 24 W--
K01(d)
C--
    [[Image:{{{P6-netimage}}}|50px]] File:Hexagonal bipyramid.png
octagonal prism
{{{P8-name2}}}
Octagonal dipyramid
{{{P8-dual2}}}
U76(f) P8:Op
2 8 | 2
2 2 4 |

     
     
     
     

4.4.8
8{4}+2{8}
F=10
E=24
V=16
D8h, [8,2], (*822), order 32 W--
K01(f)
C--
    [[Image:{{{P8-netimage}}}|50px]]  
decagonal prism
{{{P10-name2}}}
Decagonal dipyramid
{{{P10-dual2}}}
U76(h) P10:Dip
2 10 | 2
2 2 5 |

     
     
     
     

4.4.10
10{4}+2{10}
F=12
E=30
V=20
D10h, [10,2], (*10.2.2), order 40 W--
K01(h)
C--
    [[Image:{{{P10-netimage}}}|50px]]  
dodecagonal prism
{{{P12-name2}}}
Dodecagonal dipyramid
{{{P12-dual2}}}
U76(j) P12:Twip
2 12 | 2
2 2 6 |

     
     
     
     

4.4.12
12{4}+2{12}
F=14
E=36
V=24
D12h, [12,2], (*12.2.2), order 48 W--
K01(j)
C--
    [[Image:{{{P12-netimage}}}|50px]] File:Dodecagonal dipyramid.png
triangular antiprism
{{{AP3-name2}}}
Trigonal trapezohedron
{{{AP3-dual2}}}
U77(a) AP3:Oct
| 2 2 3

     
     

3.3.3.3
6{3}+2{3}
F=8
E=12
V=6
D3d, [6,2+], (2*3), order 18 W--
K02(a)
C--
    [[Image:{{{AP3-netimage}}}|50px]]  
square antiprism
{{{AP4-name2}}}
Tetragonal trapezohedron
{{{AP4-dual2}}}
U77(b) AP4:Squap
| 2 2 4

     
     

3.3.3.4
8{3}+2{4}
F=10
E=16
V=8
D4d, [2+,8], (2*4), order 16 W--
K02(b)
C--
    [[Image:{{{AP4-netimage}}}|50px]]  
pentagonal antiprism
{{{AP5-name2}}}
Pentagonal trapezohedron
{{{AP5-dual2}}}
U77(c) AP5:Pap
| 2 2 5

     
     

3.3.3.5
10{3}+2{5}
F=12
E=20
V=10
D5d, [2+,10], (2*5), order 20 W--
K02(c)
C--
    [[Image:{{{AP5-netimage}}}|50px]]  
hexagonal antiprism
{{{AP6-name2}}}
Hexagonal trapezohedron
{{{AP6-dual2}}}
U77(d) AP6:Hap
| 2 2 6

     
     

3.3.3.6
12{3}+2{6}
F=14
E=24
V=12
D6d, [2+,12], (2*6), order 24 W--
K02(d)
C--
    [[Image:{{{AP6-netimage}}}|50px]]  
octagonal antiprism
{{{AP8-name2}}}
Octagonal trapezohedron
{{{AP8-dual2}}}
U77(f) AP8:Oap
| 2 2 8

     
     

3.3.3.8
16{3}+2{8}
F=18
E=32
V=16
D8d, [2+,16], (2*8), order 32 W--
K02(f)
C--
    [[Image:{{{AP8-netimage}}}|50px]]  
decagonal antiprism
{{{AP10-name2}}}
Decagonal trapezohedron
{{{AP10-dual2}}}
U77(h) AP10:Dap
| 2 2 10

      
     

3.3.3.10
20{3}+2{10}
F=22
E=40
V=20
D10d, [2+,20], (2*10), order 40 W--
K02(h)
C--
    [[Image:{{{AP10-netimage}}}|50px]]  
dodecagonal antiprism
{{{AP12-name2}}}
Dodecagonal trapezohedron
{{{AP12-dual2}}}
U77(j) AP12:Twap
| 2 2 12

      
     

3.3.3.12
24{3}+2{12}
F=26
E=48
V=24
D12d, [2+,24], (2*12), order 48 W--
K02(j)
C--
    [[Image:{{{AP12-netimage}}}|50px]]  

Nonconvex prisms and antiprisms

edit
pentagrammic prism
{{{P5d2-name2}}}
Pentagrammic dipyramid
{{{P5d2-dual2}}}
U78(a) P5d2:Stip
2 5/2 | 2

       

4.4.5/2
5{4}+2{5/2}
F=7
E=15
V=10
D5h, [5,2], (*522), order 20 W--
K03(a)
C--
    [[Image:{{{P5d2-netimage}}}|50px]] File:Pentagrammic dipyramid.png
pentagrammic antiprism
{{{AP5d2-name2}}}
Pentagrammic trapezohedron
{{{AP5d2-dual2}}}
U79(a) AP5d2:Stap
| 2 2 5/2

       

3.3.3.5/2
10{3}+2{5/2}
F=12
E=20
V=10
D5h, [5,2], (*552), order 20 W--
K04(a)
C--
    [[Image:{{{AP5d2-netimage}}}|50px]] File:Pentagrammic trapezohedron.png
pentagrammic crossed-antiprism
{{{AP5d3-name2}}}
Pentagrammic concave trapezohedron
{{{AP5d3-dual2}}}
U80(a) AP5d3:Starp
| 2 2 5/3

       
=       

3.3.3.5/3 or 3.3.3.-5/2
10{3}+2{5/2}
F=12
E=20
V=10
D5h, [5,2], (*522), order 20 W--
K05(a)
C--
    [[Image:{{{AP5d3-netimage}}}|50px]] File:Pentagrammic concave trapezohedron.png

Uniform tilings

edit

Us:Squat
4 | 2 4

     
     
     
       
       
       

Square tiling
4.4.4.4 (or 44)
p4m, [4,4], (*442)      Dual:self-dual

Uts:Tosquat
2 | 4 4
4 4 2 |

     
      or    

Truncated square tiling
4.8.8
p4m, [4,4], (*442)      Dual:Tetrakis square tiling

Uns:Snasquat
| 4 4 2

     
      or    

Snub square tiling
3.3.4.3.4
p4g, [4+,4], (4*2)      Dual:Cairo pentagonal tiling

Uh:Hexat
3 | 6 2
2 6 | 3
3 3 3 |

     
     
   

Hexagonal tiling
6.6.6 (or 63)
p6m, [6,3], (*632)      Dual:Triangular tiling

Uht:That
2 | 6 3
3 3 | 3

     
    =      

Trihexagonal tiling
(3.6)2
p6m, [6,3], (*632)      Dual:Rhombille tiling

Uth:Toxat
2 3 | 6

     

Truncated hexagonal tiling
3.12.12
p6m, [6,3], (*632)      Dual:Triakis triangular tiling

Ut:Trat
6 | 3 2
3 | 3 3
| 3 3 3

     
     
    =      
   

Triangular tiling
3.3.3.3.3.3 (or 36)
p6m, [6,3], (*632)      Dual:Hexagonal tiling

Urth:Rothat
3 | 6 2

     

Rhombitrihexagonal tiling
3.4.6.4
p6m, [6,3], (*632)      Dual:Deltoidal trihexagonal tiling

Ugrth:Othat
2 6 3 |

     

Truncated trihexagonal tiling
4.6.12
p6m, [6,3], (*632)      Dual:Kisrhombille tiling

Unh:Snathat
| 6 3 2

     

Snub trihexagonal tiling
3.3.3.3.6
p6, [6,3]+, (632)      Dual:Floret pentagonal tiling

Uet:Etrat
2 | 2 (2 2)

       
       

Elongated triangular tiling
3.3.3.4.4
cmm, [∞,2+,∞], (2*22)      Dual:Prismatic pentagonal tiling

TEST |- | [[{{{{{{1}}}-name}}}]]

| [[Image:{{{{{{1}}}-image}}}|50px]] | {{{{{{1}}}-Wythoff}}} | | [[Image:{{{{{{1}}}-vfigimage}}}|40px]]
{{{{{{1}}}-vfig}}} | {{{{{{1}}}-group}}} | {{{{{{1}}}-B}}} | W{{{{{{1}}}-W}}} | U{{{{{{1}}}-U}}} | K{{{{{{1}}}-K}}} | C{{{{{{1}}}-C}}} | {{{{{{1}}}-V}}} | {{{{{{1}}}-E}}} | {{{{{{1}}}-F}}} | {{{{{{1}}}-chi}}} | {{{{{{1}}}-Fdetail}}}