fix construction of tetrahedron

@@ -245,29 +245,25 @@ where T: Add<Output = T> + Sub<Output = T> + Neg<Output = T>
         }
     }
 
-    // https://rechneronline.de/pi/tetrahedron.php
+    // construct via cube, see polyhedra.pdf
     pub fn tetrahedron(a :T) -> Polyeder<T> {
-        let  f0 :T = 0.into();
-        let  f3 :T = 3.into();
-        let  f4 :T = 4.into();
-        let  f6 :T = 6.into();
-        let f12 :T = 12.into();
-
-        let yi :T = a / f12 * T::sqrt(f6).unwrap();
-        let yc :T = a /  f4 * T::sqrt(f6).unwrap();
-        let zi :T = T::sqrt(f3).unwrap() / f6 * a;
-        let zc :T = T::sqrt(f3).unwrap() / f3 * a;
-        let ah :T = a / 2.into();
-
-        let ps = vec!( Point::new( f0,  yc,  f0)
-                     , Point::new(-ah, -yi, -zi)
-                     , Point::new( ah, -yi, -zi)
-                     , Point::new( f0, -yi,  zc) );
-
-        let fs = vec!( Face::new(vec!(1, 2, 3), &ps)
-                     , Face::new(vec!(1, 0, 2), &ps)
-                     , Face::new(vec!(3, 0, 1), &ps)
-                     , Face::new(vec!(2, 0, 3), &ps) );
+        let f2 :T = 2.into();
+        let ch    = a / (f2 * T::sqrt(f2).unwrap());
+
+        let ps = vec!( Point::new(-ch, -ch,  ch)    // A
+                     , Point::new(-ch,  ch, -ch)    // C
+                     , Point::new( ch, -ch, -ch)    // E
+                     , Point::new( ch,  ch,  ch) ); // G
+
+        // bottom: 1, 2, 3
+        let fs = vec!( Face::new(vec!(2, 1, 0), &ps) // bottom
+                     , Face::new(vec!(3, 2, 0), &ps)
+                     , Face::new(vec!(0, 1, 3), &ps)
+                     , Face::new(vec!(1, 2, 3), &ps) );
+        //let fs = vec!( Face::new(vec!(0, 1, 2), &ps) // bottom
+        //             , Face::new(vec!(0, 2, 3), &ps)
+        //             , Face::new(vec!(3, 1, 0), &ps)
+        //             , Face::new(vec!(3, 2, 1), &ps) );
 
         Polyeder{ points: ps, faces: fs }
     }

@@ -36,8 +36,7 @@ use fractional::trigonometry::Trig;
 use fractional::vector::Vector;
 use fractional::transform::{TMatrix, Transformable};
 use fractional::xcb::XcbEasel;
-
-use fractional::geometry::{Camera,DirectLight,Polyeder,Primitives};
+use fractional::geometry::{Camera, DirectLight, Polyeder, Primitives};
 
 fn mean(v: &Vec<i64>) -> Result<Fractional, TryFromIntError> {
     let r = v.iter().fold(0, |acc, x| acc + x);
@@ -403,10 +402,11 @@ fn main() {
     let xcb = XcbEasel::new().unwrap();
     let (tx, rx) = mpsc::channel();
 
+
     _democanvas( &xcb, "Something...(f64)", tx.clone()
                , Polyeder::triangle(60.0)
                , Polyeder::tetrahedron(80.0)
-               , Polyeder::cube(55.0)
+               , Polyeder::cube(45.0)
                , DirectLight::new(Vector(0.0, 0.0, 1.0)) );
     /*
     _democanvas( &xcb, "Something...(Fractional)", tx.clone()