  The thriving area of synthetic carbon allotropes witnesses theoretic
proposals and experimental syntheses of many new two-dimensional ultrathin
structures, which are often achieved by careful arrangement of non-hexagon
$\mathrm{sp^2}$ defects in graphene. Here, we introduce pyramid $\mathrm{sp^3}$
hybridization into $\mathrm{sp^2}$ network and propose a new carbon polymorph
with clathrate pattern and with minimum egg-tray shape (termed as clathrate
graphene). Eight symmetrically equivalent $\mathrm{sp^2}$ carbon atoms and two
symmetrically equivalent $\mathrm{sp^2}$ carbon atoms in its tetragonal
primitive unit cell form two perpendicularly oriented rectangles and four
bridging hexagons. Though deformed bond lengths and bond angles, the planar
geometry of both tetrarings and hexagons are retained. High percentage and
small deformation of hexagons make this metastable
$\mathrm{sp^2}$-$\mathrm{sp^3}$ allotrope comparable with pure $\mathrm{sp^2}$
$T$-graphene and penta-graphene in energetics. Exhaustive \textit{ab initio}
calculations confirm its dynamical and elastic stabilities, reveal its
semiconducting nature with an indirect band gap of 0.90 eV for unstressed
sample, and suggest a giant strain tuning effect which endows versatile
electronic properties ranging from metallic to semiconducting. Furthermore, we
observe multiple von Hove singularities near the Fermi energy.These salient
properties may imply potential nanoelectronic applications. These findings help
understand structure-property relationship for two-dimensional carbon
allotropes, and help search new carbon polymorphs.
