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Download as PDF; Printable version; In other projects ... This template is intended to provide consistent and easy links between Polyhedron database related templates.
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctahedron. As a parallelohedron, the rhombic dodecahedron can be used to tesselate its copies in space creating a rhombic dodecahedral honeycomb.
If a plane intersects a solid (a 3-dimensional object), then the region common to the plane and the solid is called a cross-section of the solid. [1] A plane containing a cross-section of the solid may be referred to as a cutting plane. The shape of the cross-section of a solid may depend upon the orientation of the cutting plane to the solid.
The icosidodecahedron is an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in a vertex. [5] The polygonal faces that meet for every vertex are two equilateral triangles and two regular pentagons, and the vertex figure of an icosidodecahedron is {{nowrap|(3 ...
In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry.
One way is to copy templates from a polyhedron-making book, such as Magnus Wenninger's Polyhedron Models, 1974 (ISBN 0-521-09859-9). A second way is drawing faces on paper or with computer-aided design software and then drawing on them the polyhedron's edges. The exposed nets of the faces are then traced or printed on template material.
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This means the polyhedron cannot be separated by a plane to create two small convex polyhedra with regular faces; examples of Johnson solids are the first six Johnson solids—square pyramid, pentagonal pyramid, triangular cupola, square cupola, pentagonal cupola, and pentagonal rotunda—tridiminished icosahedron, parabidiminished ...