In a monoclinic unit cell, the relation of sides and angles are respectively:

In crystallography, the monoclinic crystal system is one of the seven crystal systems. To solve this, we need to recall the defining characteristics of a monoclinic unit cell regarding the lengths of its edges (denoted as a, b, c) and the angles between them (denoted as α, β, γ).

First, for the sides (edge lengths) in a monoclinic unit cell, all three edges are of different lengths. This means that a is not equal to b, b is not equal to c, and a is not equal to c. So, we have $$a \neq b \neq c$$.

Second, for the angles, in a monoclinic system, two of the angles are exactly 90 degrees, and one angle is not equal to 90 degrees. Specifically, in the standard convention, the angle β (between the a-axis and c-axis) is not 90 degrees, while the angles α (between the b-axis and c-axis) and γ (between the a-axis and b-axis) are both 90 degrees. However, the labeling of axes can vary, and the monoclinic system can be described equivalently by having any one angle not equal to 90 degrees while the other two are 90 degrees, as long as the side lengths are unequal.

Now, let's examine the given options:

Option A states: a = b $$\neq$$ c and $$\alpha = \beta = \gamma = 90$$°. This describes a tetragonal system, where two sides are equal and all angles are 90 degrees, which is not monoclinic.

Option B states: a $$\neq$$ b $$\neq$$ c and $$\alpha = \beta = \gamma = 90$$°. This describes an orthorhombic system, where all sides are unequal but all angles are 90 degrees, which is not monoclinic.

Option C states: a $$\neq$$ b $$\neq$$ c and $$\beta = \gamma = 90$$° $$\neq \alpha$$. This means the sides are all unequal, and angles β and γ are 90 degrees, while α is not 90 degrees. Although the standard monoclinic system has β not equal to 90 degrees (with α and γ at 90 degrees), this option describes a valid monoclinic system because the geometry is equivalent under a relabeling of axes. For example, if we swap the b and c axes, the non-right angle becomes α, matching this description. Thus, this option correctly represents the monoclinic system.

Option D states: a $$\neq$$ b $$\neq$$ c and $$\alpha \neq \beta \neq \gamma \neq 90$$°. This describes a triclinic system, where all angles are different and not 90 degrees, which is not monoclinic.

Therefore, after comparing all options, Option C matches the monoclinic unit cell characteristics when considering the flexibility in axis labeling.

Hence, the correct answer is Option C.