後はこれなんかどう？
xp = ParametricPlot3D[{t Sqrt[1 - z^2], Sqrt[1 - z^2], z}, {z, -1, 1}, {t, -1, 1}];
xm = ParametricPlot3D[{t Sqrt[1 - z^2], -Sqrt[1 - z^2], z}, {z, -1,1}, {t, -1, 1}];
yp = ParametricPlot3D[{Sqrt[1 - z^2], t Sqrt[1 - z^2], z}, {z, -1,1}, {t, -1, 1}];
ym = ParametricPlot3D[{-Sqrt[1 - z^2], t Sqrt[1 - z^2], z}, {z, -1,1}, {t, -1, 1}];
Show[xp, xm, yp, ym, PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}}]

式の意味は自分で解読してね。
ちょっと格好つけて
xp = ParametricPlot3D[{t Sqrt[1 - z^2], Sqrt[1 - z^2], z}, {z, -1, 1}, {t, -1, 1}, PlotStyle -> Opacity[0.5], Mesh -> None];
xm = ParametricPlot3D[{t Sqrt[1 - z^2], -Sqrt[1 - z^2], z}, {z, -1,1}, {t, -1, 1}, PlotStyle -> Opacity[0.5], Mesh -> None];
yp = ParametricPlot3D[{Sqrt[1 - z^2], t Sqrt[1 - z^2], z}, {z, -1,1}, {t, -1, 1}, PlotStyle -> Opacity[0.5], Mesh -> None];
ym = ParametricPlot3D[{-Sqrt[1 - z^2], t Sqrt[1 - z^2], z}, {z, -1,1}, {t, -1, 1}, PlotStyle -> Opacity[0.5], Mesh -> None];
Show[xp, xm, yp, ym, PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}}]
とか。