User:Tomruen/List of uniform polyhedra and tilings

See: User:Tomruen/polyhedron db testing

Convex regulars

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

Great dodecahedron {{{gD-name2}}}	Small stellated dodecahedron {{{gD-dual2}}}	U35	gD:Gad 5⁄2 | 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 5⁄2	(5⁄2)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 5⁄2 | 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 5⁄2	(5⁄2)3 12 { 5⁄2 }	F=12 E=30 V=20	Ih, H3, [5,3], (*532)	W22 K57 C68			[[Image:{{{gsD-netimage}}}|50px]]

Semiregulars

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

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

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

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

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

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}}}