Highlight the intersection between a convex hull and a triangle in 3d

I am trying to highlight the intersection between a convex hull and a triangle in 3d. The corresponding code is

 %ConvexHull
 X = [1 0 0; 0 1 0;0 0 1;0.85 0.85 0;0.85 0 0.85;0 0.85 0.85;0.75 0.75 0.75]; %# involves a 3D point on each row  
 K = convhulln(X);
 H=trisurf(K,X(:,1),X(:,2),X(:,3),'FaceColor', 'interp','EdgeAlpha',0.1)
 alpha(H, 0.8)

 hold on

 %Triangle
 pointA=[1.75 0 0];
 pointB=[0 1.75 0];
 pointC=[0 0 1.75];
 points=[pointA' pointB' pointC']; % using the data given in the question
 P=fill3(points(1,:),points(2,:),points(3,:),'g')
 grid on
 alpha(P, 0.4)

which produces the following figure

I think this figure is not completely clear, especially the intersection part. Any idea or hint to enhance it?