\[\begin{xy} 0; <1em ,0em>: (1,1);p+/v a(18) 5.5em/**@{-}, (1,3);p+/v a(18) 5.5em/**@2{-}, (1,5);p+/v a(18) 5.5em/**@3{-},\end{xy} \] \[ \begin{xy} \xymatrix { U_a \ar@/_/[ddr]_y \ar@{.>}[dr]|{\langle x,y \rangle} \ar@/^/[drr]^x \\ & X \times_Z Y \ar[d]^q \ar[r]_p & X \ar[d]_f \\ & Y \ar[r]^g & Z } \end{xy} \] \[ \begin{xy} (0,30)*{正６面体＝立方体}="A", (0,0)*{\bullet}="A", (18,12)*{\bullet}="A", (-18,12)*{\bullet}="A", (18,-6)*{\bullet}="A", (-18,-6)*{\bullet}="A", (0,-18)*{\bullet}="A", (0,6)*{\bullet}="A", (0,24)*{\bullet}="A", {(0,0) \ar @{-}(18,12)}, {(0,0) \ar @{-}(0,-18)}, {(0,0) \ar @{-}(-18,12)}, {(0,24) \ar @{-}(18,12)}, {(0,24) \ar @{-}(-18,12)}, {(18,12) \ar @{-}(18,-6)}, {(-18,12) \ar @{-}(-18,-6)}, {(0,-18) \ar @{-}(18,-6)}, {(0,-18) \ar @{-}(-18,-6)}, {(0,6) \ar @{.}(18,-6)}, {(0,6) \ar @{.}(-18,-6)}, {(0,6) \ar @{.}(0,24)}, \end{xy} \]

\[\bm{x} = \frac{123}{\sum_1^n x^k}\]