  We have investigated structures of the ground and excited states of
$^{16}\textrm{O}$ with the method of variation after spin-parity projection in
the antisymmetrized molecular dynamics model combined with the generator
coordinate method of $^{12}\textrm{C}+\alpha$ cluster. The calculation
reasonably reproduces the experimental energy spectra, $E2$, $E3$, $E4$, $IS1$
transitions, and $\alpha$-decay properties. The formation of 4 $\alpha$
clusters has been confirmed from nucleon degrees of freedom in the AMD model
without assuming existence of any clusters. They form "tetrahedral" $4\alpha$-
and $^{12}\textrm{C}+\alpha$-cluster structures. The $^{12}\textrm{C}+\alpha$
structure constructs the $K^\pi=0^+$ band consisting of the $0^+_2$, $2^+_1$,
and $4^+_1$ states and the $K^\pi=0^-$ band of the $1^-_2$, $3^-_2$, and
$5^-_1$ states. The $0^+_1$, $3^-_1$, and $4^+_2$ states are assigned to the
ground band constructed from the tetrahedral 4$\alpha$ structure. The $0^+_1$
and $3^-_1$ are approximately interpreted as $T_d$ band members with the ideal
tetrahedral configuration. The ground state $4\alpha$ correlation plays an
important role in enhancement of the $E3$ transition strength to the $3^-_1$.
The $4^+_2$ state is not the ideal $T_d$ member but constructed from a
distorted tetrahedral $4\alpha$ structure. Moreover, significant state mixing
of the tetrahedral $4\alpha$ and $^{12}\textrm{C}+\alpha$ cluster structures
occurs between $4^+_1$ and $4^+_2$ states, indicating that the $T_d$
configuration of $4\alpha$ is rather fragile at $J^\pi=4^+$.
