Newman Projection with t-butyl group? So again in Chapter 4 David Klein book, we have this organic molecule with a t-butyl group (just as an aside, this is t-butyl ethane, right?



Now how is it that the correct Newman projection must be the following?


What I glean from the Lewis structure is that because there are no wedges or dashed lines, the methyl groups ought to be in the same plane. How can there be a methyl group jutting out upwards and to the right, and another methyl group jutting out upwards and to the left in the t-butyl group and not be illustrated as such with dashed lines and wedges? Thanks in advance!
Lewis structures and skeletal structures show which atoms are connected to which other atoms, and the type of bonds (single, double, triple). They do not show the shape (geometry) of the molecule.

For example, the two skeletal structures below refer to the same molecule, butane:



When there is ambiguity (i.e. multiple molecules with the same skeletal structure), you can add information about the stereochemistry by adding dashes bonds and wedges. In your case, the molecule is achiral, so that does not apply.

To figure out the geometry, remember that carbon atoms with four single bonds have a tetrahedral geometry. You get other geometries when there is a double bond (trigonal planar) or a triple bond (linear) or other, more unusual features associated with a carbon atom (lone pair, non-zero formal charge, radicals, two double bonds).