In geometry

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 small dodecahemicosacron is the dual of the small dodecahemicosahedron

Small dodecahemicosahedron

In geometry, the small dodecahemicosahedron is a nonconvex uniform polyhedron, indexed as U62. Its vertex figure is a crossed quadrilateral.It is a hemipolyhedron with ten hexagonal faces passing through the model center.- Related polyhedra :...

, and is one of nine dual hemipolyhedra. It appears visually indistinct from the great dodecahemicosacron

Great dodecahemicosacron

In geometry, the great dodecahemicosacron is the dual of the great dodecahemicosahedron, and is one of nine dual hemipolyhedra. It appears visually indistinct from the small dodecahemicosacron....

.

Since the small dodecahemicosahedron has ten hexagonal faces

Face (geometry)

In geometry, a face of a polyhedron is any of the polygons that make up its boundaries. For example, any of the squares that bound a cube is a face of the cube...

 passing through the model center, the small dodecahemicosacron has ten vertices

Vertex (geometry)

In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...

 at infinity. In Magnus Wenninger

Magnus Wenninger

Father Magnus J. Wenninger OSB is a mathematician who works on constructing polyhedron models, and wrote the first book on their construction.-Early life and education:...

's Dual Models, they are represented with intersecting infinite prisms

Prism (geometry)

In geometry, a prism is a polyhedron with an n-sided polygonal base, a translated copy , and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a...

 passing through the model center, cut off at a certain point that is convenient for the maker.

See also

• Hemi-icosahedron
  Hemi-icosahedron
  A hemi-icosahedron is an abstract regular polyhedron, containing half the faces of a regular icosahedron. It can be realized as a projective polyhedron , which can be visualized by constructing the projective plane as a hemisphere where opposite points along the boundary are connected and dividing...
  
  - The ten vertices at infinitity correspond directionally to the 10 vertices of this abstract polyhedron.