I wrote the definition but I can't find the figure of cone.
In $R^2$ , the cones related to strict componentwise order, weak component wise order and lexicographic order and max order?
Strict componentwise order : $y^1 <y^2 \iff y_1^k <y_2^k \forall k=1,2 $
weak component wise order : $y^1\leq y^2 \iff y_1^k <= y_2^k \forall k=1,2$
lexicographic order : $k^* = min \{k: y_1^k \neq y_2^k\} $ , $y^1 <_lex y^2 \iff y_1^k* < y_2^k* $ or $y^1=y^2$
Max order: $y^1 <_max y^2 \iff max y_1^k < max y_2^k$
For all order we have a related cone , with notation $C_R$ , $C_R=\{y^2-y^1 : y^1 R y^2\} $.