Great icosihemidodecahedron
Encyclopedia
In geometry
, the great icosihemidodecahedron is a nonconvex uniform polyhedron
, indexed as U71. Its vertex figure
is a crossed quadrilateral.
It is a hemipolyhedron
with 6 decagrammic faces passing through the model center.
is the icosidodecahedron
. It also shares its edge arrangement with the great icosidodecahedron (having the triangular faces in common), and with the great dodecahemidodecahedron
(having the decagrammic faces in common).
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 icosihemidodecahedron is a nonconvex uniform polyhedron
Nonconvex uniform polyhedron
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting...
, indexed as U71. Its vertex figure
Vertex figure
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
is a crossed quadrilateral.
It is a hemipolyhedron
Hemipolyhedron
In geometry, a hemipolyhedron is a uniform star polyhedron some of whose faces pass through its center. These "hemi" faces lie parallel to the faces of some other symmetrical polyhedron, and their count is half the number of faces of that other polyhedron - hence the "hemi" prefix.The prefix "hemi"...
with 6 decagrammic faces passing through the model center.
Related polyhedra
Its convex hullConvex hull
In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X....
is the icosidodecahedron
Icosidodecahedron
In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon...
. It also shares its edge arrangement with the great icosidodecahedron (having the triangular faces in common), and with the great dodecahemidodecahedron
Great dodecahemidodecahedron
In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U70. Its vertex figure is a crossed quadrilateral....
(having the decagrammic faces in common).
 Great icosidodecahedron |
 Great dodecahemidodecahedron Great dodecahemidodecahedron In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U70. Its vertex figure is a crossed quadrilateral.... |
 Great icosihemidodecahedron |
 Icosidodecahedron Icosidodecahedron In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon... (convex hull Convex hull In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X.... ) |