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From the paper cited in the previous slide.
The authors write:
"It may seem surprising that [under uniaxial compression (compression in the vertical direction)] the spheres buckle around the equator. After all, by common experience if a spherical shell is placed between two flat plates and compressed, which is a superficially similar mode of deformation, the spheres tend to buckle at the poles. However, compressing spherical shells between flat plates induces a different pattern of stresses in the shell from embedding them in a [uniaxially compressed] elastic material. An embedded spherical shell, under uniaxial compression at infinity, is in [hoop] compression around the equator while in tension around the poles; this is why buckling occurs around the equator."
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