  We identify the possibility of realizing higher order topological (HOT)
phases in noncrystalline or amorphous materials. Starting from two and three
dimensional crystalline HOT insulators, accommodating topological corner
states, we gradually enhance structural randomness in the system. Within a
parameter regime, as long as amorphousness is confined by outer crystalline
boundary, the system continues to host corner states, yielding amorphous HOT
insulators. However, as structural disorder percolates to the edges, corner
states start to dissolve into amorphous bulk, and ultimately the system becomes
a trivial insulator when amorphousness plagues the entire system. These
outcomes are further substantiated by computing the quadrupolar (octupolar)
moment in two (three) dimensions. Therefore, HOT phases can be realized in
amorphous solids, when wrapped by a thin (lithographically grown, for example)
crystalline layer. Our findings suggest that crystalline topological phases can
be realized even in the absence of local crystalline symmetry.
