The glabrous skin of the rhinarium (naked nose) of many mammalian species exhibit a polygonal pattern of grooves that retain physiological fluid, thereby keeping their nose wet and, among others, facilitating the collection of chemosensory molecules. In this talk, I will discuss how rhinarial polygonal domains are not placode-derived skin appendages but arise through a self-organized mechanical process consisting in the constrained growth and buckling of epidermal layers, coupled with an underlying network of stiff blood vessels. Numerical simulations demonstrate that the mechanical stress generated by excessive epidermal growth concentrates at the positions of vessels which form rigid base points, causing the epidermal layers to move outwards and shape domes — akin to arches rising against stiff pillars. Remarkably, this gives rise to a larger length scale (the distance between the vessels) in the surface folding pattern than would otherwise occur in the absence of vessels. These results are linked to the concept of ‘mechanical positional information’, by which material properties of anatomical elements impose local contraints to an otherwise globally self-organized mechanical pattern. In addition, analyses of the rhinarial patterns in cow clones highlight a substantial level of stochasticity of the pre-pattern of vessels, while numerical simulations recapitulate the disruption of the folding pattern in cows affected by a hereditary disorder that causes hyperextensibility of the skin.