February 2006 : ← - January - February - March - April - May - June - July - August - September - October - November - December- → 1 February 2006 (Wednesday) Governor of West Virginia Joe Manchin asks for a halt in coal mining following two more coal mining deaths in the state that saw fourteen people die in coal mining disasters in... Download high resolution version (819x791, 71 KB)Icosahedron, made by me using POV-Ray, see image:poly. ...

A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a total of 120 symmetries including transformations that combine a reflection and a rotation. A regular dodecahedron has the same set of symmetries, since it is the dual of the icosahedron. An icosahedron [ˌaıkəsəhiːdrən] noun (plural: -drons, -dra [-drə]) is a polyhedron having 20 faces, but usually a regular icosahedron is meant. ... A dodecahedron is literally a polyhedron with 12 faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve pentagonal faces, with three meeting at each vertex. ...

The group of symmetries that includes reflections is S₅, or the group of permutations of five objects, since there is exactly one such symmetry for each permutation of the five pairs of diametrically opposite vertices. The set of orientation-preserving symmetries forms a group referred to as A₅.

Details

The icosahedral rotation group I with fundamental domain

Apart from the two infinite series of prismatic and antiprismatic symmetry, rotational icosahedral symmetry or chiral icosahedral symmetry of chiral objects and full icosahedral symmetry or achiral icosahedral symmetry are the discrete point symmetries (or equivalently, symmetries on the sphere) with the largest symmetry groups. In mathematics, given a lattice Γ in a Lie group G, a fundamental domain is a set D of representatives for the cosets G/Γ, that is also a well-behaved set topologically, in a sense that can be made precise in one of several ways. ... A discrete point group in 3D is a finite symmetry group in 3D that leaves the origin fixed. ... // List of symmetry groups on the sphere Spherical symmetry groups are also called point groups (in 3D). ... The symmetry group of an object (e. ...

Icosahedral symmetry is not compatible with translational symmetry, so there are no associated crystallographic point groups or space groups. The icosahedral rotation group I is of order 60. The group I is isomorphic to A₅, the alternating group on 5 objects. The group contains 5 versions of T_h with 20 versions of D₃ (10 axes, 2 per axis), and 6 versions of D₅. A translation slides an object by a vector a: Ta(p) = p + a. ... In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ... The space group of a crystal is a mathematical description of the symmetry inherent in the structure. ... In mathematics, an isomorphism (in Greek isos = equal and morphe = shape) is a kind of interesting mapping between objects. ... In mathematics an alternating group is the group of even permutations of a finite set. ... 5 (five) is the natural number following 4 and preceding 6. ...

The full icosahedral group I_h has order 120. It has I as normal subgroup of index 2. The group I_h is isomorphic to I × C₂, or A₅ × C₂, with the inverse corresponding to element (identity,1). The group contains 10 versions of D_3d and 6 versions of D_5d (symmetries like antiprisms). In mathematics, a normal subgroup N of a group G is a subgroup invariant under conjugation; that is, for each element n in N and each g in G, the element g−1ng is still in N. The statement N is a normal subgroup of G is written: . There are... In mathematics, if G is a group, H a subgroup of G, and g an element of G, then gH = { gh : h an element of H } is a left coset of H in G, and Hg = { hg : h an element of H } is a right coset of H in G...

Presentations Arthur Moritz Schönflies (April 17, 1853 Landsberg an der Warthe(Gorzów) – May 27, 1928) was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology. ... H(arold). ... To meet Wikipedias quality standards, this article or section may require cleanup. ... In mathematics, one method of defining a group is by a presentation. ...

I:

I_h:

Note that other presentations are possible.

In the disdyakis triacontahedron one full face is a fundamental domain; other solids with the same symmetry can be obtained by adjusting the orientation of the faces, e.g. flattening selected subsets of faces to combine each subset into one face, or replacing each face by multiple faces, or a curved surface.

The icosahedral group I_h with fundamental domain

Download high resolution version (812x847, 130 KB)Disdyakis triacontahedron, made by me using POV-Ray, see image:poly. ... Download high resolution version (812x847, 130 KB)Disdyakis triacontahedron, made by me using POV-Ray, see image:poly. ... A disdyakis triacontahedron, or hexakis icosahedron is the Catalan solid whose Archimedean dual is the truncated icosidodecahedron. ...

Conjugacy classes

The conjugacy classes of I are: In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure. ...

• identity
• 12 × rotation by 72°
• 12 × rotation by 144°
• 20 × rotation by 120°
• 15 × rotation by 180°

Those of I_h include also each with inversion:

• inversion
• 12 × rotoreflection by 108°
• 12 × rotoreflection by 36°
• 20 × rotoreflection by 60°
• 15 × reflection

Subgroups

I contains 5 copies of T.

I_h contains 5 copies of T_h.

Solids with full icosahedral symmetry

(For details see below.)

Platonic_solid - regular polyhedra (all faces of the same type) In solid geometry and some ancient physical theories, a Platonic solid is a convex polyhedron with all its faces being congruent regular polygons, and the same number of faces meeting at each of its vertices. ...

Archimedean solids - polyhedra with more than one polygon face type. In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ...

3.10.10

4.6.10

5.6.6

3.4.5.4

3.5.3.5

Catalan_solids - duals of the Archimedean solids. Download high resolution version (876x802, 67 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Download high resolution version (868x869, 105 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Download high resolution version (878x874, 80 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Download high resolution version (858x871, 113 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Download high resolution version (841x861, 76 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... A rhombic dodecahedron In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. ...

V3.10.10

V4.6.10

V5.6.6

V3.4.5.4

V3.5.3.5

Download high resolution version (819x849, 107 KB)Triakis icosahedron, made by me using POV-Ray, see image:poly. ... Download high resolution version (812x847, 130 KB)Disdyakis triacontahedron, made by me using POV-Ray, see image:poly. ... Download high resolution version (844x843, 106 KB)Pentakis dodecahedron, made by me using POV-Ray, see image:poly. ... Download high resolution version (854x843, 102 KB)Deltoidal hexecontahedron, made by me using POV-Ray, see image:poly. ... Download high resolution version (780x859, 88 KB)Rhombic triacontahedron, made by me using POV-Ray, see image:poly. ...

Platonic solids

Name	Picture	Faces	Edges	Vertices	Edges per face	Faces meeting at each vertex
dodecahedron	( Animation) A Platonic solid is a convex polyhedron whose faces all use the same regular polygon and such that the same number of faces meet at all its vertices. ... A dodecahedron is literally a polyhedron with 12 faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve pentagonal faces, with three meeting at each vertex. ... Download high resolution version (847x829, 63 KB)Dodecahedron, made by me using POV-Ray, see image:poly. ... Spinning dodecahedron, first 17 frames accidentally rendered with flashiness=1, while last 43 are rendered with flashiness=0. ...	12	30	20	5	3
icosahedron	( Animation) An icosahedron [ˌaıkəsəhiːdrən] noun (plural: -drons, -dra [-drə]) is a polyhedron having 20 faces, but usually a regular icosahedron is meant. ... Download high resolution version (819x791, 71 KB)Icosahedron, made by me using POV-Ray, see image:poly. ... Spinning icosahedron, made by me using POV-Ray, see image:poly. ...	20	30	12	3	5

Achiral Archimedean solids

Name	picture	Faces		Edges	Vertices	Vertex configuration
icosidodecahedron (quasi-regular: vertex- and edge-uniform)	( Video)	32	20 triangles 12 pentagons	60	30	3,5,3,5
truncated dodecahedron	( Video)	32	20 triangles 12 decagons	90	60	3,10,10
truncated icosahedron or commonly football (soccer ball)	( Video)	32	12 pentagons 20 hexagons	90	60	5,6,6
rhombicosidodecahedron or small rhombicosidodecahedron	( Video)	62	20 triangles 30 squares 12 pentagons	120	60	3,4,5,4
truncated icosidodecahedron or great rhombicosidodecahedron	( Video)	62	30 squares 20 hexagons 12 decagons	180	120	4,6,10

In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ... An icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. ... Download high resolution version (841x861, 76 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Spinning icosidodecahedron, made by me using POV-Ray, see image:poly. ... In geometry, a pentagon is any five-sided polygon. ... The truncated dodecahedron is an Archimedean solid. ... Download high resolution version (876x802, 67 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Spinning truncated dodecahedron, made by me using POV-Ray, see :image:poly. ... An image of a Regular Decagon In geometry, a decagon is any polygon with ten sides and ten angles, and usually refers to a regular decagon, having all sides of equal length and all angles equal to 144°. Its Schläfli symbol is {10}. The area of a regular decagon... The truncated icosahedron is an Archimedean solid. ... Download high resolution version (878x874, 80 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Spinning truncated icosahedron, made by me using POV-Ray, see :image:poly. ... A colored model The rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid. ... Download high resolution version (858x871, 113 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Spinning truncated tetrahedron, made by me using POV-Ray, see image:poly. ... The truncated icosidodecahedron, or great rhombicosidodecahedron, is an Archimedean solid. ... Download high resolution version (868x869, 105 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Spinning truncated tetrahedron, made by me using POV-Ray, see image:poly. ...

Achiral Catalan solids

Name	picture	Dual Archimedean solid	Faces	Edges	Vertices	Face Polygon
rhombic triacontahedron (quasi-regular dual: face- and edge-uniform)	( Video)	icosidodecahedron	30	60	32	rhombus
triakis icosahedron	( Video)	truncated dodecahedron	60	90	32	isosceles triangle
pentakis dodecahedron	( Video)	truncated icosahedron	60	90	32	isosceles triangle
deltoidal hexecontahedron	(Video)	rhombicosidodecahedron	60	120	62	kite
disdyakis triacontahedron or hexakis icosahedron	( Video)	truncated icosidodecahedron	120	180	62	scalene triangle

A rhombic dodecahedron In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. ... The Rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. ... Download high resolution version (780x859, 88 KB)Rhombic triacontahedron, made by me using POV-Ray, see image:poly. ... Spinning rhombic triacontahedron, made by me using POV-Ray, see image:poly. ... An icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. ... This shape is a rhombus In geometry, a rhombus (also known as a rhomb) is a quadrilateral in which all of the sides are of equal length. ... A triakis icosahedron is a catalan solid, the dual polyhedron to the truncated icosahedron. ... Download high resolution version (819x849, 107 KB)Triakis icosahedron, made by me using POV-Ray, see image:poly. ... Spinning triakis icosahedron, made by me using POV-Ray, see image:poly. ... The truncated dodecahedron is an Archimedean solid. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... A pentakis dodecahedron is a catalan solid which looks a bit like an overinflated dodecahedron. ... Download high resolution version (844x843, 106 KB)Pentakis dodecahedron, made by me using POV-Ray, see image:poly. ... Spinning pentakis dodecahedron, made by me using POV-Ray, see image:poly. ... The truncated icosahedron is an Archimedean solid. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... A deltoidal hexecontahedron is a catalan solid which looks a bit like an overinflated dodecahedron. ... Download high resolution version (854x843, 102 KB)Deltoidal hexecontahedron, made by me using POV-Ray, see image:poly. ... A colored model The rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid. ... A separate article is about kite flying. ... A disdyakis triacontahedron, or hexakis icosahedron is the Catalan solid whose Archimedean dual is the truncated icosidodecahedron. ... Download high resolution version (812x847, 130 KB)Disdyakis triacontahedron, made by me using POV-Ray, see image:poly. ... Spinning disdyakis triacontahedron, made by me using POV-Ray, see image:poly. ... The truncated icosidodecahedron, or great rhombicosidodecahedron, is an Archimedean solid. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ...

Kepler-Poinsot solids

A Kepler solid (also called Kepler-Poinsot solid) is a regular non-convex polyhedron, all the faces of which are identical regular polygons and which has the same number of faces meeting at all its vertices (compare to Platonic solids). ... Image File history File links Kepler_poinsot_solids. ...

Achiral nonconvex uniform polyhedra

Image File history File links Download high resolution version (641x640, 21 KB) Summary Small ditrigonal icosidodecahedron, U30 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 18 KB) Summary Small icosicosidodecahedron, U31 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 17 KB) Summary Small dodecicosidodecahedron, U33 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (639x641, 18 KB) Summary Small stellated dodecahedron, U34 Licensing File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Great_dodecahedron. ... Image File history File links Download high resolution version (640x640, 19 KB) Summary Dodecadodecahedron, U36 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x639, 27 KB) Summary Rhombidodecadodecahedron, U38 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 18 KB) Summary Small rhombidodecahedron, U39 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 24 KB) Summary Ditrigonal dodecadodecahedron, U41 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 8 KB) Summary Great ditrigonal dodecicosidodecahedron, U42 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 21 KB) Summary Small ditrigonal dodecicosidodecahedron, U43 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 27 KB) Summary Icosidodecadodecahedron, U44 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 24 KB) Summary Icositruncated dodecadodecahedron, U45 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 23 KB) Summary Image of Great Ditrigonal Icosidodecahedron, U47 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 31 KB) Summary Great icosicosidodecahedron, U48 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 16 KB) Summary Small icosihemidodecahedron, U49 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (641x641, 21 KB) Summary Small dodecicosahedron, U50 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (638x639, 14 KB) Summary Small dodecahemidodecahedron, U51 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 17 KB) Summary Great stellated dodecahedron, U52 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 21 KB) Summary Image of concave regular polyhedron, great Icosahedron, U53. ... Image File history File links Download high resolution version (640x640, 20 KB) Summary Great icosidodecahedron, U54 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 23 KB) Summary Great truncated icosahedron, U55 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 27 KB) Summary Rhombicosahedron, U56 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 24 KB) Summary Small stellated truncated dodecahedron, U58 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x639, 29 KB) Summary Truncated dodecadodecahedron, U59 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x641, 27 KB) Summary Great dodecicosidodecahedron, U61 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x639, 22 KB) Summary Small dodecahemicosahedron, U62 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 29 KB) Summary Great dodecicosahedron, U63 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 20 KB) Summary Great dodecahemicosahedron, U65 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (639x640, 21 KB) Summary Great stellated truncated dodecahedron, U66 External Links VRML model 1 VRML model 2 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 40 KB) Summary Great truncated icosidodecahedron, U68 External Links VRML model 1 VRML model 2 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (639x640, 23 KB) Summary Great dodecahemidodecahedron, U70 External Links VRML model 1 VRML model 2 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x639, 21 KB) Summary Great icosihemidodecahedron, U71 External Links VRML model 1 VRML model 2 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (640x640, 32 KB) Summary Great rhombidodecahedron, U73 External Links VRML model 1 VRML model 2 Licensing I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high resolution version (848x816, 55 KB) Summary Great dirhombicosidodecahedron, U75, K80 Licensing External Links VRML Model 1 K80 VRML Model 2 K80 File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Download high resolution version (848x819, 33 KB) Summary Small snub icosicosidodecahedron, U32 Sources VRML model 1 VRML model 2 Licensing File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Download high resolution version (771x754, 51 KB) Summary Small retrosnub icosicosidodecahedron, U72, K77 Licensing External Links = VRML model 1 K77 VRML model 2 K77 File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

Chiral Archimedean and Catalan solids

Snub dodecahedron (Ccw)

Pentagonal hexecontahedron (Ccw)

Archimedean solids: Download high resolution version (853x866, 121 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Download high resolution version (853x866, 121 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... The snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid. ... Download high resolution version (834x851, 98 KB)Pentagonal hexecontahedron (Ccw), made by me using POV-Ray, see image:poly. ... Download high resolution version (834x851, 98 KB)Pentagonal hexecontahedron (Ccw), made by me using POV-Ray, see image:poly. ... A pentagonal hexecontahedron is a Catalan solid which looks a bit like an icosahedron undergoing cell division. ... In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ...

Name	picture	Faces		Edges	Vertices	Vertex configuration
snub dodecahedron or snub icosidodecahedron (2 chiral forms)	( Video) ( Video)	92	80 triangles 12 pentagons	150	60	3,3,3,3,5

Catalan solids: The snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid. ... Download high resolution version (853x866, 121 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Spinning snub dodecahedron (ccw), made by me using POV-Ray, see image:poly. ... Download high resolution version (872x877, 116 KB)Somethingahedron, made by me using POV-Ray, see image:poly. ... Spinning snub dodecahedron (cw), made by me using POV-Ray, see image:poly. ... A rhombic dodecahedron In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid. ...

Name	picture	Dual Archimedean solid	Faces	Edges	Vertices	Face Polygon
pentagonal hexecontahedron	( Video)( Video)	snub dodecahedron	60	150	92	irregular pentagon

Stellated Archimedean solids: A pentagonal hexecontahedron is a Catalan solid which looks a bit like an icosahedron undergoing cell division. ... Download high resolution version (834x851, 98 KB)Pentagonal hexecontahedron (Ccw), made by me using POV-Ray, see image:poly. ... Download high resolution version (846x841, 96 KB)Pentagonal hexecontahedron (Cw), made by me using POV-Ray, see image:poly. ... Spinning pentagonal hexecontahedron (ccw), made by me using POV-Ray, see image:poly. ... Spinning pentagonal hexecontahedron (cw), made by me using POV-Ray, see image:poly. ... The snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid. ... In geometry, a pentagon is any five-sided polygon. ...

• the snub dodecadodecahedron
• the great inverted snub icosidodecahedron or great vertisnub icosidodecahedron
• the great retrosnub icosidodecahedron or great inverted retrosnub icosidodecahedron

Chiral nonconvex uniform polyhedra

Image File history File links Download high resolution version (846x818, 39 KB) Summary Snub dodecadodecahedron, U40, K45 Sources VRML model 1 K45 VRML model 2 K45 Licensing File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Download high resolution version (846x814, 38 KB) Summary Snub icosidodecadodecahedron, U46, K51 Licensing External links VRML model 1 K51 VRML model 2 K51 File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Download high resolution version (844x828, 37 KB) Summary Great snub icosidodecahedron, U57, K62 Licensing External links VRML model 1 K62 VRML model 2 K62 File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Download high resolution version (845x822, 32 KB) Summary Inverted snub dodecadodecahedron, U60, K65 Licensing External links = VRML model 1 K65 VRML model 2 K65 File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Download high resolution version (844x835, 42 KB) Summary Great snub dodecicosidodecahedron, U64, K69 Licensing == External links == VRML model 1 K69 VRML model 2 K69 File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Download high resolution version (800x812, 39 KB) Summary Great inverted snub icosidodecahedron, U69, K74 Licensing External links VRML model 1 K74 VRML model 2 K74 File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Download high resolution version (805x842, 54 KB) Summary Great retrosnub icosidodecahedron, U74, K79 Licensing External links VRML model 1 K79 VRML model 2 K79 File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

See also

• Polyhedral compound