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What would cyclopropane look like if it weren't planar?

How and why does non-planar cyclopropane have higher torsional strain than planar cyclopropane? can you please show me visually via image that non-planar cyclopropane has higher torisional strain and maybe more angle strain than planar cyclopropane?

On the otherhand, why and how is cyclobutane bulged or puckering, a.k.a non-planar?

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    $\begingroup$ Considering that three points define a plane, geometrically, it's not really possible for cyclopropane to be non-planar... $\endgroup$ – a-cyclohexane-molecule Oct 17 '16 at 4:31
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Why is cyclopropane planar?

This is like asking why $\ce{HCl}$ is linear–just as two points define a line, three points define a plane. There isn't any way to orient the three methylene groups in space that they aren't coplanar.

$\hspace{8cm}$plane

Torsional strain in cyclopropane is also significant for this reason (the molecule has a $\mathrm{C_3}$ axis through the center of the ring, meaning every hydrogen is overlapping). Any reduction in torsional strain, however, decreases the already weak carbon-carbon $\ce{sp^3}$ orbital overlap. Though the $\ce{C-C-C}$ bond angles are $60º$, the orbitals are still oriented roughly $109.5º$ from one another, resulting in very weak and highly strained banana bonds.

$\hspace{8cm}$strain

Why is cyclobutane nonplanar?

Cyclobutane has one additional methylene, and can reduce its torsional strain by orienting one methylene out of the plane of the other three.

$\hspace{7.3cm}$cyclobutane

This is in part possible due to the much greater carbon-carbon $\ce{sp^3}$ orbital overlap.

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  • $\begingroup$ Due to symmetry, the carbon in cyclopropane is not $sp^3$ but $sp^2$ hybridized. $\endgroup$ – Deathbreath Nov 14 '16 at 19:03
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If cyclopropane did pucker then a new plane would exist. This is because any set of three points (a.k.a three carbons) is coplanar. Cyclobutane puckering can occur and make a difference as a set of four points/carbons is not necessarily coplanar.

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