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  2. Cross section (geometry) - Wikipedia

    en.wikipedia.org/wiki/Cross_section_(geometry)

    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.

  3. Icosidodecahedron - Wikipedia

    en.wikipedia.org/wiki/Icosidodecahedron

    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 ...

  4. Rhombic dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombic_dodecahedron

    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.

  5. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    A central cross section of a regular tetrahedron is a square. The two skew perpendicular opposite edges of a regular tetrahedron define a set of parallel planes. When one of these planes intersects the tetrahedron the resulting cross section is a rectangle. [11] When the intersecting plane is near one of the edges the rectangle is long and skinny.

  6. Ten-of-diamonds decahedron - Wikipedia

    en.wikipedia.org/wiki/Ten-of-diamonds_decahedron

    The ten-of-diamonds can be dissected in an octagonal cross-section between the two rhombic faces. It is a decahedron with 12 vertices, 20 edges, and 10 faces (4 triangles, 4 trapezoids, 1 rhombus, and 1 isotoxal octagon). Michael Goldberg labels this polyhedron 10-XXV, the 25th in a list of space-filling decahedra. [2]

  7. List of uniform polyhedra - Wikipedia

    en.wikipedia.org/wiki/List_of_uniform_polyhedra

    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.

  8. Parallelohedron - Wikipedia

    en.wikipedia.org/wiki/Parallelohedron

    A plesiohedron is a broader class of three-dimensional space-filling polyhedra, formed from the Voronoi diagrams of periodic sets of points. [9] As Boris Delaunay proved in 1929, [ 14 ] every parallelohedron can be made into a plesiohedron by an affine transformation, [ 2 ] but this remains open in higher dimensions, [ 1 ] and in three ...

  9. 24-cell - Wikipedia

    en.wikipedia.org/wiki/24-cell

    Net. In four-dimensional geometry, the 24-cell is the convex regular 4-polytope [1] (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,4,3}. It is also called C 24, or the icositetrachoron, [2] octaplex (short for "octahedral complex"), icosatetrahedroid, [3] octacube, hyper-diamond or polyoctahedron, being constructed of octahedral cells.

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