Great rhombic triacontahedron
Encyclopedia
In geometry
, the great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron
. It is the dual
of the great icosidodecahedron (U54). It has 30 intersecting rhombic
faces.
The great rhombic triacontahedron can be constructed by expanding the size of the faces of a rhombic triacontahedron
by a factor of
, with 
being the golden ratio
.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
. It is the dual
Dual polyhedron
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another...
of the great icosidodecahedron (U54). It has 30 intersecting rhombic
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.
The great rhombic triacontahedron can be constructed by expanding the size of the faces of a rhombic triacontahedron
Rhombic triacontahedron
In geometry, the rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. It is an Archimedean dual solid, or a Catalan solid. It is the polyhedral dual of the icosidodecahedron, and it is a zonohedron....
by a factor of
, with being the golden ratioGolden ratio
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989...
.