Rhombic icosahedron
Type	zonohedron Zonohedron A zonohedron is a convex polyhedron where every face is a polygon with point symmetry or, equivalently, symmetry under rotations through 180°. Any zonohedron may equivalently be described as the Minkowski sum of a set of line segments in three-dimensional space, or as the three-dimensional...
Face polygon	rhombus Rhombus In Euclidean geometry, a rhombus or rhomb is a convex quadrilateral whose four sides all have the same length. The rhombus is often called a diamond, after the diamonds suit in playing cards, or a lozenge, though the latter sometimes refers specifically to a rhombus with a 45° angle.Every...
Faces	20 rhombi
Edges	40
Vertices	22
Faces per vertex	3, 4 and 5
Dual Polyhedron	Irregular-faced pentagonal gyrobicupola Pentagonal gyrobicupola In geometry, the pentagonal gyrobicupola is one of the Johnson solids . Like the pentagonal orthobicupola , it can be obtained by joining two pentagonal cupolae along their bases...
Symmetry group Symmetry group The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...	D5d
Properties	convex Convex set In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object... , zonohedron Zonohedron A zonohedron is a convex polyhedron where every face is a polygon with point symmetry or, equivalently, symmetry under rotations through 180°. Any zonohedron may equivalently be described as the Minkowski sum of a set of line segments in three-dimensional space, or as the three-dimensional...

A rhombic icosahedron (or rhombic icosacontahedron) is a polyhedron

Polyhedron

In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...

 shaped like an oblate sphere

Sphere

A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

.

It is composed of 20 rhombic faces, of which three, four, or five meet at each vertex. It has 10 faces on the polar axis with 10 rhombi following the equator.

Even though all the faces are congruent, the rhombic icosahedron is not face-transitive, since one may distinguish whether a particular face is near the equator or a pole by examining the types of vertices surrounding that face.

The rhombic icosahedron is a zonohedron

Zonohedron

A zonohedron is a convex polyhedron where every face is a polygon with point symmetry or, equivalently, symmetry under rotations through 180°. Any zonohedron may equivalently be described as the Minkowski sum of a set of line segments in three-dimensional space, or as the three-dimensional...

 that is dual to an irregular-faced pentagonal gyrobicupola

Pentagonal gyrobicupola

In geometry, the pentagonal gyrobicupola is one of the Johnson solids . Like the pentagonal orthobicupola , it can be obtained by joining two pentagonal cupolae along their bases...

.

It has D_5d

Dihedral symmetry in three dimensions

This article deals with three infinite sequences of point groups in three dimensions which have a symmetry group that as abstract group is a dihedral group Dihn .See also point groups in two dimensions.Chiral:...

 symmetry.

External links

• http://www.georgehart.com/virtual-polyhedra/zonohedra-info.html
  • VRML
    VRML
    VRML is a standard file format for representing 3-dimensional interactive vector graphics, designed particularly with the World Wide Web in mind...
    
    Model http://www.georgehart.com/virtual-polyhedra/vrml/rhombic_icosahedron.wrl