List of uniform polyhedra

There are 75 non-prismatic uniform polyhedra, not including the infinite families of polygonal prisms and antiprisms. 5 are regular and convex, 4 are regular and nonconvex, 13 are nonregular and convex, and 53 are nonregular and nonconvex.

A large amount of near-miss uniform polyhedra may also be constructed. These polyhedra are isogonal and all of their faces are either regular or almost regular. Some of the near-misses are semi-uniform.

Name	Short Name	Image	Coxeter Diagram	Vertex Type	Vertices	Edges	Faces	Army	Regiment	Symmetry	Dihedral angles
Tetrahedron	tet		x3o3o	3.3.3	4	6	4 triangles	Tetrahedron	Tetrahedron	A3	3-3: $\arccos\left( \frac{1}{3} \right) \approx 70.52878°$
Truncated tetrahedron	tut		x3x3o	3.6.6	12	18	4 triangles 4 hexagons	Truncated tetrahedron	Truncated tetrahedron		6-3: $\arccos\left( -\frac{1}{3} \right) \approx 109.47122°$ 6-6: $\arccos\left( \frac{1}{3} \right) \approx 70.52878°$
Cube	cube		x4o3o	4.4.4	8	12	6 squares	Cube	Cube	B3	4-4: $90°$
Truncated cube	tic		x4x3o	3.8.8	24	36	8 triangles 6 octagons	Truncated cube	Truncated cube		8-3: $\arccos\left( -\frac{\sqrt{3}}{3} \right) \approx 125.26439°$ 8-8: $90°$
Great cubicuboctahedron	gocco		x4/3x3o4*a	8/3.3.8/3.4	24	48	8 triangles 6 squares 6 octagrams		Great cubicuboctahedron		8/3-3: $\arccos\left( -\frac{\sqrt{3}}{3} \right) \approx 125.26439°$ 8/3-4: $90°$
Quasirhombicuboctahedron	querco		x4/3o3x	4.3/2.4.4	24	48	8 triangles 6+12 squares				4-4: $45°$ 4-3: $\arccos\left( \frac{\sqrt{6}}{3} \right) \approx 35.26439°$
Great rhombihexahedron	groh			4.8/3.4/3.8/5	24	48	12 squares 6 octagrams				8/3-4 #1: $90°$ 8/3-4 #2: $45°$
Cuboctahedron	co		o4x3o	3.4.3.4	12	24	8 triangles 6 squares	Cuboctahedron	Cuboctahedron		4-3: $\arccos\left( -\frac{\sqrt{3}}{3} \right) \approx 125.26439°$
Octahemioctahedron	oho		x3/2o3x3*a	6.3/2.6.3	12	24	8 triangles 4 hexagons				6-3: $\arccos\left( \frac{1}{3} \right) \approx 70.52878°$
Cubohemioctahedron	cho		(o4/3x3x4*a)/2	6.4/3.6.4	12	24	6 squares 4 hexagons				6-4: $\arccos\left( \frac{\sqrt{3}}{3} \right) \approx 54.73561°$
Truncated octahedron	toe		o4x3x	4.6.6	24	36	6 squares 8 hexagons	Truncated octahedron	Truncated octahedron		6-4: $\arccos\left( -\frac{\sqrt{3}}{3} \right) \approx 125.26439°$ 6-6: $\arccos\left( -\frac{1}{3} \right) \approx 109.47122°$
Octahedron	oct		o4o3x	3.3.3.3	6	12	8 triangles	Octahedron	Octahedron		3-3: $\arccos\left( -\frac{1}{3} \right) \approx 109.47122°$
Tetrahemihexahedron	thah		(x3/2o3x)/2	4.3/2.4.3	6	12	4 triangles 3 squares			A3	3-3: $\arccos\left( \frac{\sqrt{3}}{3} \right) \approx 54.73561°$
Quasitruncated hexahedron	quith		x4/3x3o	8/3.8/3.3	24	36	8 triangles 6 octagrams	Small rhombicuboctahedron	Quasitruncated hexahedron	B3	8/3-8/3: $90°$ 8/3-3: $\arccos\left( \frac{\sqrt{3}}{3} \right) \approx 54.73561°$
Small rhombicuboctahedron	sirco		x4o3x	3.4.4.4	24	48	8 triangles 6+12 squares		Small rhombicuboctahedron		4-3: $\arccos\left( -\frac{\sqrt{6}}{3} \right) \approx 144.73561°$ 4-4: $135°$
Small cubicuboctahedron	socco		x4/3o3x4*a	8.3/2.8.4	24	48	8 triangles 6 squares 6 octagons				8-4: $90°$ 8-3: $\arccos\left( \frac{\sqrt{3}}{3} \right) \approx 54.73561°$
Small rhombihexahedron	sroh			4.8.4/3.8/7	24	48	12 squares 6 octagons				8-4 #1: $90°$ 8-4 #2: $45°$
Great rhombicuboctahedron	girco		x4x3x	4.6.8	48	72	12 squares 8 hexagons 6 octagons	Great rhombicuboctahedron	Great rhombicuboctahedron		6-4: $\arccos\left( -\frac{\sqrt{6}}{3} \right) \approx 144.73561°$ 8-4: $135°$ 8-6: $\arccos\left( -\frac{\sqrt{3}}{3} \right) \approx 125.26439°$
Cubitruncated cuboctahedron	cotco		x4/3x3x4*a	8/3.6.8	48	72	8 hexagons 6 octagons 6 octagrams	Semi-uniform great rhombicuboctahedron	Cuboctatruncated cuboctahedron		8/3-6: $\arccos\left( -\frac{\sqrt{3}}{3} \right) \approx 125.26439°$ 8/3-8: $90°$ 8-6: $\arccos\left( -\frac{\sqrt{3}}{3} \right) \approx 125.26439°$
Quasitruncated cuboctahedron	quitco		x4/3x3x	8/3.4.6/5	48	72	12 squares 8 hexagons 6 octagrams	Semi-uniform great rhombicuboctahedron	Quasitruncated cuboctahedron		8/3-4: $135°$ 8/3-6: $\arccos\left( \frac{\sqrt{3}}{3} \right) \approx 54.73561°$ 6-4: $\arccos\left( \frac{\sqrt{6}}{3} \right) \approx 35.26439°$
Snub cube	snic		s4s3s	3.3.3.3.4	24	60	8+24 triangles 6 squares	Snub cube	Snub cube	B3+	3-3: $\approx 53.23459°$ 4-3: $\approx 142.98343°$
Dodecahedron	doe		x5o3o	5.5.5	20	30	12 pentagons	Dodecahedron	Dodecahedron	H3	5-5: $\arccos\left( -\frac{\sqrt{5}}{5} \right) \approx 116.56505°$
Great stellated dodecahedron	gissid		x5/2o3o	5/2.5/2.5/2	20	30	12 pentagrams		Great stellated dodecahedron		5/2-5/2: $\arccos\left( \frac{\sqrt{5}}{5} \right) \approx 63.43495°$
Small ditrigonary icosidodecahedron	sidtid		x5/2o3o3*a	5/2.3.5/2.3.5/2.3	20	60	20 triangles 12 pentagrams		Small ditrigonary icosidodecahedron		5/2-3: $\arccos\left( -\sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 142.62263°$
Ditrigonary dodecadodecahedron	ditdid		x5/3o3o5*a	5/3.5.5/3.5.5/3.5	20	60	12 pentagons 12 pentagrams				5-5/2: $\arccos\left( \frac{\sqrt{5}}{5} \right) \approx 63.43495°$
Great ditrigonary icosidodecahedron	gidtid		x3/2o3o5*a	(5.3.5.3.5.3)/2	20	60	20 triangles 12 pentagons				5-3: $\arccos\left( -\sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 142.62263°$
Truncated dodecahedron	tid		x5x3o	3.10.10	60	90	20 triangles 12 decagons	Truncated dodecahedron	Truncated dodecahedron		10-3: $\arccos\left( -\sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 142.62263°$ 10-10: $\arccos\left( -\frac{\sqrt{5}}{5} \right) \approx 116.56505°$
Great ditrigonal dodecicosidodecahedron	gidditdid		x5/3x3o5*a	10/3.3.10/3.5	60	120	20 triangles 12 pentagons 12 decagrams		Great ditrigonal dodecicosidodecahedron		3-10/3: $\arccos\left( -\sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 142.62263°$ 5-10/3: $\arccos\left( -\frac{\sqrt{5}}{5} \right) \approx 116.56505°$
Great icosicosidodecahedron	giid		o3/2x3x5*a	6.3/2.6.5	60	120	20 triangles 12 pentagons 20 hexagons				5-6: $\arccos\left( \sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 79.18768°$ 3-6: $\arccos\left( -\frac{\sqrt{5}}{3} \right) \approx 41.81032°$
Great dodecicosahedron	giddy			6.10/3.6/5.10/7	60	120	20 hexagons 12 decagrams				6-10/3 #1: $\arccos\left( -\sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 142.62263°$ 6-10/3 #2: $\arccos\left( \sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 37.37737°$
Small inverted retrosnub icosicosidodecahedron	sirsid		s5/2s3/2s3/2*a	(3.3.3.3.3.5/3)/2	60	180	60 triangles 20 hexagrams 12 pentagrams	Semi-uniform truncated dodecahedron	Small inverted retrosnub icosicosidodecahedron		5/2–3: $\arccos\left(\sqrt{\frac{15-2\sqrt5-2\sqrt{30\sqrt5-65}}{15}}\right) ≈ 44.45753°$ 3–3: $\arccos\left(\frac{\sqrt{3+2\sqrt5}}{3}\right) ≈ 24.33196°$
Icosidodecahedron	id		o5x3o	3.5.3.5	30	60	20 triangles 12 pentagons	Icosidodecahedron	Icosidodecahedron		3-5: $\arccos\left( -\sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 142.62263°$
Small dodecahemidodecahedron	sidhid		(x5/4o5x5*a)/2	10.5/4.10.5	30	60	12 pentagons 6 decagons				5-10: $\arccos\left( \frac{\sqrt{5}}{5} \right) \approx 63.43495°$
Small icosihemidodecahedron	seihid		(x3/2o3x5*a)/2	10.3/2.10.3	30	60	20 triangles 6 decagons				3-10: $\arccos\left( \sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 37.37737°$
Dodecadodecahedron	did		o5/2x5o	5/2.5.5/2.5	30	60	12 pentagons 12 pentagrams		Dodecadodecahedron		5-5/2: $\arccos\left( -\frac{\sqrt{5}}{5} \right) \approx 116.56505°$
Great dodecahemicosahedron	gidhei		(o5/4x3x5*a)/2	6.5/4.6.5	30	60	12 pentagons 10 hexagons				5-6: $\arccos\left( \sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 37.37737°$
Small dodecahemicosahedron	sidhei		(x5/3o5/2x3*a)/2	6.5/3.6.5/2	30	60	12 pentagrams 10 hexagons				5-5/2: $\arccos\left( \sqrt{\frac{5-2\sqrt{5}}{15}} \right) \approx 79.18768°$
Great icosidodecahedron	gid		o5/2x3o	5/2.3.5/2.3	30	60	20 triangles 12 pentagrams		Great icosidodecahedron		3-5/2: $\arccos\left( \sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 37.37737°$
Great icosihemidodecahedron	geihid		(o3/2x5/3x3*a)/2	10/3.3/2.10/3.3	30	60	20 triangles 6 decagrams				3-10: $\arccos\left( \sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 37.37737°$
Great dodecahemidodecahedron	gidhid		(x5/3x5/3o5/2*a)/2	10/3.5/3.10/3.5/2	30	60	12 pentagrams 6 decagrams				5/2-10: $\arccos\left( \frac{\sqrt{5}}{5} \right) \approx 63.43495°$
Truncated icosahedron	ti		o5x3x	5.6.6	60	90	12 pentagons 20 hexagons	Truncated icosahedron	Truncated icosahedron		5-6: $\arccos\left( -\sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 142.62263°$ 6-6: $\arccos\left( -\frac{\sqrt{5}}{3} \right) \approx 138.18968°$
Truncated great dodecahedron	tigid		o5/2x5x	10.10.5/2	60	90	12 pentagrams 12 decagons	Semi-uniform truncated icosahedron	Truncated great dodecahedron		10-5/2: $\arccos\left( -\frac{\sqrt{5}}{5} \right) \approx 116.56505°$ 10-10: $\arccos\left( \frac{\sqrt{5}}{5} \right) \approx 63.43495°$
Great dodecicosidodecahedron	gaddid		x5/3x5/2o3*a	10/3.5/2.10/3.3	60	120	20 triangles 12 pentagrams 12 decagrams		Great dodecicosidodecahedron		5/2-10/3: $\arccos\left( -\frac{\sqrt{5}}{5} \right) \approx 116.56505°$ 3-10/3: $\arccos\left( -\sqrt{\frac{2-\sqrt{5}}{15}} \right) \approx 100.81232°$
Quasirhombicosidodecahedron	qrid		x5/3o3x	4.5/3.4.3	60	120	20 triangles 30 squares 12 pentagrams				4-3: $\arccos\left( \frac{\sqrt{15}-\sqrt{3}}{6} \right) \approx 69.09484°$ 5/2-4: $\arccos\left( \frac{5-\sqrt{5}}{10} \right) \approx 58.28253°$
Great rhombidodecahedron	gird			4.10/3.4/3.10/7	60	120	30 squares 12 decagrams				4-10/3 #1: $\arccos\left( \frac{5-\sqrt{5}}{10} \right) \approx 58.28253°$ 4-10/3 #2: $\arccos\left( \frac{5+\sqrt{5}}{10} \right) \approx 31.71747°$
Rhombidodecadodecahedron	raded		x5/2o5x	4.5/2.4.5	60	120	30 squares 12 pentagons 12 pentagrams	Semi-uniform truncated icosahedron	Rhombidodecadodecahedron		4-5/2: $\arccos\left( -\sqrt{\frac{5+\sqrt{5}}{10}} \right) \approx 148.28253°$ 4-5: $\arccos\left( -\sqrt{\frac{5-\sqrt{5}}{10}} \right) \approx 121.71747°$
Icosidodecadodecahedron	ided		o5/3x3x5*a	6.5/3.6.5	60	120	12 pentagons 12 pentagrams 20 hexagons				5-6: $\arccos\left( -\sqrt{\frac{5-2\sqrt{5}}{15}} \right) \approx 79.18768°$ 5/2-6: $\arccos\left( -\sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 37.37737°$
Rhombicosahedron	ri			6.4.6/5.4/3	60	120	30 squares 20 hexagons				4-6 #1: $\arccos\left( \frac{\sqrt{3}-\sqrt{15}}{6} \right) \approx 110.90516°$ 4-6 #1: $\arccos\left( \frac{\sqrt{3}+\sqrt{15}}{6} \right) \approx 20.90516°$
Small snub icosicosidodecahedron	seside		s5/2s3s3*a	3.3.3.3.3.5/2	60	180	60 triangles 20 hexagrams 12 pentagrams	Semi-uniform truncated icosahedron	Small snub icosicosidodecahedron		5/2-3: $\arccos\left(-\sqrt{\frac{15-2\sqrt5+2\sqrt{30\sqrt5-65}}{15}}\right) \approx 161.02258°$ 3-3: $\arccos\left(-\frac{\sqrt{3+2\sqrt5}}{3}\right) \approx 155.66804°$
Icosahedron	ike		o5o3x	3.3.3.3.3	12	30	20 triangles	Icosahedron	Icosahedron		3-3: $\arccos\left( -\frac{\sqrt{5}}{3} \right) \approx 138.18969°$
Great dodecahedron	gad		o5/2o5x	(5.5.5.5.5)/2	12	30	12 pentagons				5-5: $\arccos\left( \frac{\sqrt{5}}{5} \right) \approx 63.43495°$
Small stellated dodecahedron	sissid		x5/2o5o	5/2.5/2.5/2.5/2.5/2	12	30	12 pentagrams		Small stellated dodecahedron		5/2-5/2: $\arccos\left( -\frac{\sqrt{5}}{5} \right) \approx 116.56505°$
Great icosahedron	gike		o5/2o3x	(3.3.3.3.3)/2	12	30	20 triangles				3-3: $\arccos\left( \frac{\sqrt{5}}{3} \right) \approx 41.81031°$
Quasitruncated small stellated dodecahedron	quit sissid		x5/3x5o	10/3.10/3.5	60	90	12 pentagons 12 decagrams	Small rhombicosidodecahedron	Quasitruncated small stellated dodecahedron		10/3-10/3: $\arccos\left( -\frac{\sqrt{5}}{5} \right) \approx 116.56505°$ 5-10/3: $\arccos\left( \frac{\sqrt{5}}{5} \right) \approx 63.43495°$
Small rhombicosidodecahedron	srid		x5o3x	3.4.5.4	60	120	20 triangles 30 squares 12 pentagons		Small rhombicosidodecahedron		4-3: $\arccos\left( -\frac{\sqrt{3}+\sqrt{15}}{6} \right) \approx 159.09484°$ 4-5: $\arccos\left( -\sqrt{\frac{5+\sqrt{5}}{10}} \right) \approx 148.28253°$
Small dodecicosidodecahedron	saddid		x3/2o5x5*a	10.3/2.10.5	60	120	20 triangles 12 pentagons 12 decagons				5-10: $\arccos\left( \frac{\sqrt{5}}{5} \right) \approx 63.43495°$ 3-10: $\arccos\left( \sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 37.37737°$
Small rhombidodecahedron	sird			10.4.10/9.4/3	60	120	30 squares 12 decagons				4-10 #1: $\arccos\left( -\sqrt{\frac{5-\sqrt{5}}{10}} \right) \approx 121.71747°$ 4-10 #2: $\arccos\left( -\sqrt{\frac{5+\sqrt{5}}{10}} \right) \approx 148.28253°$
Truncated great icosahedron	tiggy		o5/2x3x	6.6.5/2	60	90	12 pentagrams 20 hexagons	Semi-uniform small rhombicosidodecahedron	Truncated great icosahedron		6-5/2: $\arccos\left( -\sqrt{\frac{5-2\sqrt{5}}{15}} \right) \approx 100.81232°$ 6-6: $\arccos\left( \frac{\sqrt{5}}{3} \right) \approx 41.81031°$
Small icosicosidodecahedron	siid		x5/2o3x3*a	6.5/2.6.3	60	120	20 triangles 12 pentagrams 20 hexagons	Semi-uniform small rhombicosidodecahedron	Small icosicosidodecahedron		5/2-6: $\arccos\left( -\sqrt{\frac{5+2\sqrt{5}}{15}} \right) \approx 142.62263°$ 3-6: $\arccos\left( -\frac{\sqrt{5}}{3} \right) \approx 38.18969°$
Small ditrigonal dodecicosidodecahedron	sidditdid		x5/3o3x5*a	10.5/3.10.3	60	120	20 triangles 12 pentagrams 12 decagons				3-10: $\arccos\left( \sqrt{\frac{5-2\sqrt{5}}{15}} \right) \approx 100.81232°$ 5/2-10: $\arccos\left( \frac{\sqrt{5}}{4} \right) \approx 63.43495°$
Small dodecicosahedron	siddy			10.6.10/9.6/5	60	120	20 hexagons 12 decagons				6-10 #1: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) \approx 79.18768°$ 6-10 #2: $\arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737°$
Quasitruncated great stellated dodecahedron	quit gissid		x5/3x3o	10/3.10/3.3	60	90	20 triangles 12 decagrams		Quasitruncated great stellated dodecahedron		10/3–3: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) \approx 79.18768°$ 10/3–10/3: $\arccos\left(\frac{\sqrt5}{5}\right) \approx 63.43494°$
Great dirhombicosidodecahedron	gidrid		s3s5/2s3/2s5/3*aØ*c *bØ*d	(4.5/3.4.3.4.5/2.4.3/2)/2	60	240	40 triangles 60 squares 24 pentagrams	Semi-uniform small rhombicosidodecahedron	Great dirhombicosidodecahedron		5/2–4: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{5}}\right) ≈ 71.03929°$ 3–4: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561°$
Great snub dodecicosidodecahedron	gisdid		s5/3s5/2s3*a	3.3.3.5/3.3.5/2	60	180	20+60 triangles 24 pentagrams		Great snub dodecicosidodecahedron	H3+	5/2–3 #1: $\arccos\left(-\sqrt{\frac{5+2\sqrt5-4\sqrt{5\sqrt5-10}}{15}}\right) ≈ 125.77490°$ 3–3: $\arccos\left(-\frac13\right) ≈ 109.47122°$ 5/2–3 #2: $\arccos\left(\sqrt{\frac{5+2\sqrt5+4\sqrt{5\sqrt5-10}}{15}}\right) ≈ 16.30368°$
Great rhombicosidodecahedron	grid		x5x3x	4.6.10	120	180	30 squares 20 hexagons 12 decagons	Great rhombicosidodecahedron	Great rhombicosidodecahedron	H3	6–4: $\arccos\left(-\frac{\sqrt3+\sqrt{15}}{6}\right) ≈ 159.09484°$ 10–4: $\arccos\left(-\sqrt{\frac{5+\sqrt5}{10}}\right) ≈ 148.28253°$ 10–6: $\arccos\left(-\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 142.62263°$
Icositruncated dodecadodecahedron	idtid		x5/3x3x5*a	10/3.6.10	120	180	20 hexagons 12 decagons 12 decagrams	Semi-uniform great rhombicosidodecahedron	Icosidodecatruncated icosidodecahedron		10/3–6: $\arccos\left(-\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 142.62263°$ 10–10/3: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$ 10–6: $\arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 100.81232°$
Quasitruncated dodecadodecahedron	quitdid		x5/3x5x	10/3.4.10/9	120	180	30 squares 12 decagons 12 decagrams	Semi-uniform great rhombicosidodecahedron	Quasitruncated dodecadodecahedron		10/3–4: $\arccos\left(-\sqrt{\frac{5+\sqrt5}{10}}\right) ≈ 148.28253°$ 10–10/3: $\arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495°$ 10–4: $\arccos\left(\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 58.28253°$
Great quasitruncated icosidodecahedron	gaquatid		x5/3x3x	10/3.4.6	120	180	30 squares 20 hexagons 12 decagrams	Semi-uniform great rhombicosidodecahedron	Great quasitruncated icosidodecahedron		10/3–4: $\arccos\left(-\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 121.71747°$ 10/3–6: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18768°$ 6–4: $\arccos\left(\frac{\sqrt{15}-\sqrt3}{6}\right) ≈ 69.09484°$
Snub dodecahedron	snid		s5s3s	3.3.3.3.5	60	150	20+60 triangles 12 pentagons	Snub dodecahedron	Snub dodecahedron	H3+	3-3: $\approx 164.17537°$ 5-3: $\approx 152.92992°$
Snub dodecadodecahedron	siddid		s5/2s5s	3.3.5/2.3.5	60	150	60 triangles 12 pentagons 12 pentagrams	Non-uniform snub dodecahedron	Snub dodecadodecahedron		5–3: $\approx 129.79515°$ 3–3: $\approx 151.48799°$ 5/2–3: $\approx 157.77792°$
Inverted snub dodecadodecahedron	isdid		s5/3s5s	3.5/3.3.3.5	60	150	60 triangles 12 pentagons 12 pentagrams	Non-uniform snub dodecahedron	Inverted snub dodecadodecahedron		3–3: $\approx 130.49074°$ 5-3: $\approx 68.64088°$ 5/2-3: $\approx 11.12448°$
Great snub icosidodecahedron	gosid		s5/2s3s	3.3.3.3.5/2	60	150	20+60 triangles 12 pentagrams	Non-uniform snub dodecahedron	Great snub icosidodecahedron		5/2–3: $\approx 138.82237°$ 3–3: $\approx 126.82315°$
Great inverted snub icosidodecahedron	gisid		s5/3s3s	3.3.3.3.5/3	60	150	20+60 triangles 12 pentagrams	Non-uniform snub dodecahedron	Great inverted snub icosidodecahedron		3–3: $\approx 89.78760°$ 5/2–3: $\approx 21.61047°$
Snub icosidodecadodecahedron	sided		s5/3s3s5*a	3.3.3.5.5/3	60	180	20+60 triangles 12 pentagons 12 pentagrams	Non-uniform snub dodecahedron	Snub icosidodecadodecahedron		3–3: $\approx 146.78125°$ 5–3: $\approx 120.43401°$ 5/2–3: $\approx 7.35214°$
Great retrosnub icosidodecahedron	girsid		s5/3s3/2s	(3.3.3.3.5/2)/2	60	150	20+60 triangles 12 pentagrams	Non-uniform snub dodecahedron	Great inverted retrosnub icosidodecahedron		5/2–3: $\approx 67.31029°$ 3–3: $\approx 21.72466°$

Exotic polyhedroids

Name	Short Name	Image	Coxeter Diagram	Vertex Type	Vertices	Edges	Faces	Army	Regiment	Symmetry	Dihedral angles
Small complex icosidodecahedron(ike + gad)	cid		o5/3o3x5*a	(3.5.3.5.3.5.3.5.3.5)/2	12	30*2	20 triangles 12 pentagons	Icosahedron	Icosahedron	H3
Great complex icosidodecahedron(sissid + gike)	gacid		o5/3x3o5*a	(3.5/2.3.5/2.3.5/2.3.5/2.3.5/2)/2	12	30*2	20 triangles 12 pentagrams	Icosahedron	Great icosahedron
Small complex rhombicosidodecahedron(sidtid + 5 cubes)	sicdatrid		x3o5/2x	3(3.4.5/2.4)	20	60*2	20 triangles 30 squares 12 pentagrams	Dodecahedron	sidtid
Complex rhombidodecadodecahedron(ditdid + 5 cubes)	cadditradid		x5/3o5x				12 pentagons 30 squares 12 pentagrams
Great complex rhombicosidodecahedron(gidtid + 5 cubes)	gicdatrid		x3/2o5x				20 triangles 30 squares 12 pentagons
Great disnub dirhombidodecahedron	gidisdrid				60	120+120+120	120 triangles 60 squares 24 pentagrams	Semi-uniform Srid	Gidrid