Final answer:
The question seems to ask for the nets of various 3D shapes. Nets are flat 2D figures that, when folded, form the surfaces of 3D shapes. The sphere cannot be represented by a net, while the cube, pyramid, cylinder, cone, and rectangular prism each have distinct net configurations composed of flat shapes like rectangles, squares, and circles.
Step-by-step explanation:
The question seems to be mixing concepts between shapes and their nets with some additional information about geometric properties and symmetry. The net of a 3D shape is a two-dimensional figure that, when folded, forms the surface of the 3D shape. Below are the nets for some basic 3D shapes:
- A sphere does not have a true net because it cannot be laid out flat without distortion.
- A cube consists of 6 squares that can be joined edge to edge to form its net.
- A pyramid with a square base would have a net composed of that square plus four triangular sides that meet at the apex.
- A cylinder has a net made up of two circles (the bases) and a rectangular side that wraps around to form the curved surface.
- The net of a cone includes one circle (base) and a sector of a larger circle that forms the cone's surface when rolled up.
- A rectangular prism has a net which is composed of six rectangles, or some combination of rectangles and squares.
For other information presented in the question such as symmetrical shapes like the icosahedron, or lattice structures such as square and hexagonal lattices, we can note specific geometric or symmetry properties they possess. For instance, a cube has C4 axes and C3 axes that describe its rotational symmetry around perpendicular edges and diagonal lines, respectively.