My research aims to reveal and discuss several findings related to the tessellations and space-fillings of an extremely unique and relatively new geometrical shape- spidrons. Spidrons are irregularly-shaped geometrical figures created out of numerous triangles according to a system of rules. The first section deals with a planar spidron, in which the convexity and conformity of angles allows only some spidrons- the square and hexagonal spidrons, to be tessellated into the two-dimensional space. Upon tiling, the planar system generates a dynamic, regular geometrical construction with extraordinary features. Following that, we probe into the investigation of space-filling of the 3-dimensional space with spidronal polyhedrons, which can be formed by spidrons that are creased to be assembled into three-dimensional structures in a process called deformation. Research done here on spidrons, with its remarkable planar and spatial properties, strives to open up new possibilities in the realm of geometrical design and artistic expression.