This image shows how a symmetrical organization can be more visually satisfying. 

University of Michigan - Ann Arbor

Symmetry is mostly used for aesthetic balance on a site. Designers should work to find a balance between asymmetry and symmetry on an interface, so that the user is not bored by the interface nor overwhelmed. 

Symmetry in Interaction

"What are Gestalt Principles?" Interaction Design. https://www.interaction-design.org/literature/topics/gestalt-principles

Gestalt Principles of Design

This image shows how symmetry can be used to design a visually appealing interface

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