これでしょうか。
Ex　Ey　Ezをいじれば回転しますが
隠線処理は適宜\iiiemPaintをコメントアウトしてください。

% TruncatedOctahedron.tex
\documentclass{jarticle}
\usepackage{emathP}
\begin{document}
\allinethickness{1pt}
\begin{Zahyou*}[ul=20mm,%
Ex={r(1,-145)},Ey={r(1,-25)},%
Ez={(0,1)}](-1,1)(-1,1)(-1,1)
\iiitenretu*{%
A(-0.31622777,-0.54772256,0.77459667);
B(-0.63245553,0.00000000,0.77459667);
C(-0.31622777,0.54772256,0.77459667);
D(0.31622777,0.54772256,0.77459667);
E(0.63245553,-0.00000000,0.77459667);
F(0.31622777,-0.54772256,0.77459667);
G(-0.31622777,-0.91287093,0.25819889);
H(-0.94868330,0.18257419,0.25819889);
I(-0.63245553,0.73029674,0.25819889);
J(0.63245553,0.73029674,0.25819889);
K(0.94868330,0.18257419,0.25819889);
L(0.31622777,-0.91287093,0.25819889);
M(-0.63245553,-0.73029674,-0.25819889);
N(-0.94868330,-0.18257419,-0.25819889);
O(-0.31622777,0.91287093,-0.25819889);
P(0.31622777,0.91287093,-0.25819889);
Q(0.94868330,-0.18257419,-0.25819889);
R(0.63245553,-0.73029674,-0.25819889);
S(-0.31622777,-0.54772256,-0.77459667);
T(-0.63245553,0.00000000,-0.77459667);
U(-0.31622777,0.54772256,-0.77459667);
V(0.31622777,0.54772256,-0.77459667);
W(0.63245553,-0.00000000,-0.77459667);
X(0.31622777,-0.54772256,-0.77459667)
}
\iiiTakakkei{\A\G\L\F}
\iiiTakakkei{\A\F\E\D\C\B}
\iiiTakakkei{\A\B\H\N\M\G}
\iiiTakakkei{\B\C\I\H}
\iiiTakakkei{\C\D\J\P\O\I}
\iiiTakakkei{\D\E\K\J}
\iiiTakakkei{\E\F\L\R\Q\K}
\iiiTakakkei{\G\M\S\X\R\L}
\iiiTakakkei{\H\I\O\U\T\N}
\iiiTakakkei{\J\K\Q\W\V\P}
\iiiTakakkei{\M\N\T\S}
\iiiTakakkei{\O\P\V\U}
\iiiTakakkei{\Q\R\X\W}
\iiiTakakkei{\S\T\U\V\W\X}
\end{Zahyou*}
\begin{Zahyou*}[ul=20mm,%
Ex={r(1,-145)},Ey={r(1,-25)},%
Ez={(0,1)}](-1,1)(-1,1)(-1,1)
\iiitenretu*{%
A(-0.31622777,-0.54772256,0.77459667);
B(-0.63245553,0.00000000,0.77459667);
C(-0.31622777,0.54772256,0.77459667);
D(0.31622777,0.54772256,0.77459667);
E(0.63245553,-0.00000000,0.77459667);
F(0.31622777,-0.54772256,0.77459667);
G(-0.31622777,-0.91287093,0.25819889);
H(-0.94868330,0.18257419,0.25819889);
I(-0.63245553,0.73029674,0.25819889);
J(0.63245553,0.73029674,0.25819889);
K(0.94868330,0.18257419,0.25819889);
L(0.31622777,-0.91287093,0.25819889);
M(-0.63245553,-0.73029674,-0.25819889);
N(-0.94868330,-0.18257419,-0.25819889);
O(-0.31622777,0.91287093,-0.25819889);
P(0.31622777,0.91287093,-0.25819889);
Q(0.94868330,-0.18257419,-0.25819889);
R(0.63245553,-0.73029674,-0.25819889);
S(-0.31622777,-0.54772256,-0.77459667);
T(-0.63245553,0.00000000,-0.77459667);
U(-0.31622777,0.54772256,-0.77459667);
V(0.31622777,0.54772256,-0.77459667);
W(0.63245553,-0.00000000,-0.77459667);
X(0.31622777,-0.54772256,-0.77459667)
}
\iiiemPaint<border,paintcolor=white>{\A\G\L\F}
%\iiiemPaint<border,paintcolor=white>{\A\F\E\D\C\B}
\iiiemPaint<border,paintcolor=white>{\A\B\H\N\M\G}
%\iiiemPaint<border,paintcolor=white>{\B\C\I\H}
%\iiiemPaint<border,paintcolor=white>{\C\D\J\P\O\I}
%\iiiemPaint<border,paintcolor=white>{\D\E\K\J}
%\iiiemPaint<border,paintcolor=white>{\E\F\L\R\Q\K}
\iiiemPaint<border,paintcolor=white>{\G\M\S\X\R\L}
\iiiemPaint<border,paintcolor=white>{\H\I\O\U\T\N}
%\iiiemPaint<border,paintcolor=white>{\J\K\Q\W\V\P}
\iiiemPaint<border,paintcolor=white>{\M\N\T\S}
%\iiiemPaint<border,paintcolor=white>{\O\P\V\U}
\iiiemPaint<border,paintcolor=white>{\Q\R\X\W}
\iiiemPaint<border,paintcolor=white>{\S\T\U\V\W\X}
\end{Zahyou*}
\end{document}

▼関連発言
│
└◆1265:準正多面体 [imai] 02/25 19:55
　└◆1266:Re:準正多面体 [田中徹] 02/26 01:04
　　└◆1267:Re[2]:準正多面体 [imai] 02/26 08:19
　　　├◆1268:Re[3]:準正多面体 [石原　守] 02/26 13:50
　　　│└◆1270:Re[4]:準正多面体 [石原　守] 02/26 17:48
　　　└◆1269:Re[3]:準正多面体 [田中徹] 02/26 16:14
　　　　├◆1271:Re[4]:準正多面体 [imai] 02/26 19:23
　　　　├◆1272:Re[4]:準正多面体 [飯島　徹] 02/26 19:35
　　　　│└◆1276:Re[5]:準正多面体 [田中徹] 02/26 22:24
　　　　│　└◆1279:Re[6]:準正多面体 [飯島　徹] 02/27 05:57<-last
　　　　└◆1273:Re[4]:準正多面体 [imai] 02/26 19:35
　　　　　├◆1274:Re[5]:準正多面体 [石原　守] 02/26 20:34
　　　　　│└◆1277:Re[6]:準正多面体 [imai] 02/26 22:32
　　　　　└◆1275:Re[5]:準正多面体 [田中徹] 02/26 22:10
　　　　　　└◆1278:Re[6]:準正多面体 [imai] 02/26 22:36