commit 19e04479f3e15d87c5b69e17522239f751ecca88
Author: Leszek Koltunski <leszek@koltunski.pl>
Date:   Sun May 15 23:30:32 2022 +0200

    Correct and sort the Mixup quats.

diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyMixup.java b/src/main/java/org/distorted/objectlib/objects/TwistyMixup.java
index 599c8fad..574d2fc5 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyMixup.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyMixup.java
@@ -67,78 +67,260 @@ public class TwistyMixup extends ShapeHexahedron
     {
     return new Static4D[]
       {
-      new Static4D ( 0.00000000f, 0.00000000f, 0.00000000f, 1.00000000f),
-      new Static4D ( 0.38268346f, 0.00000000f, 0.00000000f, 0.92387950f),
-      new Static4D ( 0.70710677f, 0.00000000f, 0.00000000f, 0.70710677f),
-      new Static4D ( 0.92387950f, 0.00000000f, 0.00000000f, 0.38268343f),
-      new Static4D ( 1.00000000f, 0.00000000f, 0.00000000f,-0.00000004f),
-      new Static4D ( 0.92387950f, 0.00000000f, 0.00000000f,-0.38268352f),
-      new Static4D ( 0.70710677f, 0.00000000f, 0.00000000f,-0.70710677f),
-      new Static4D ( 0.38268328f, 0.00000000f, 0.00000000f,-0.92387962f),
+      new Static4D ( 0.00000000f, 0.00000000f, 0.00000000f, 1.00000000f), // 0
+      new Static4D ( 0.00000000f, 0.00000000f, 1.00000000f, 0.00000000f), // 1
+      new Static4D ( 0.00000000f, 1.00000000f, 0.00000000f, 0.00000000f), // 2
+      new Static4D ( 1.00000000f, 0.00000000f, 0.00000000f, 0.00000000f), // 3
+
+      new Static4D ( 0.00000000f, 0.00000000f, 0.70710677f, 0.70710677f), // 4
+      new Static4D ( 0.00000000f, 0.00000000f, 0.70710677f,-0.70710677f), // 5
+      new Static4D ( 0.00000000f, 0.70710677f, 0.00000000f, 0.70710677f), // 6
+      new Static4D ( 0.00000000f, 0.70710677f, 0.00000000f,-0.70710677f), // 7
+      new Static4D ( 0.00000000f, 0.70710677f,-0.70710677f, 0.00000000f), // 8
+      new Static4D ( 0.00000000f, 0.70710677f, 0.70710677f, 0.00000000f),
+      new Static4D ( 0.70710677f, 0.00000000f, 0.00000000f, 0.70710677f), // 10
+      new Static4D ( 0.70710677f, 0.00000000f, 0.00000000f,-0.70710677f), // 11
+      new Static4D ( 0.70710677f, 0.00000000f, 0.70710677f, 0.00000000f), // 12
+      new Static4D ( 0.70710677f, 0.00000000f,-0.70710677f, 0.00000000f), // 13
+      new Static4D ( 0.70710677f,-0.70710677f, 0.00000000f, 0.00000000f),
+      new Static4D ( 0.70710677f, 0.70710677f, 0.00000000f, 0.00000000f),
+
+      new Static4D ( 0.50000000f, 0.50000000f, 0.50000000f, 0.50000000f),
+      new Static4D ( 0.50000000f, 0.50000000f, 0.50000000f,-0.50000000f),
+      new Static4D ( 0.50000000f, 0.50000000f,-0.50000000f, 0.50000000f), // 18
+      new Static4D ( 0.50000000f, 0.50000000f,-0.50000000f,-0.50000000f),
+      new Static4D ( 0.50000000f,-0.50000000f, 0.50000000f, 0.50000000f), // 20
+      new Static4D ( 0.50000000f,-0.50000000f, 0.50000000f,-0.50000000f),
+      new Static4D ( 0.50000000f,-0.50000000f,-0.50000000f, 0.50000000f),
+      new Static4D ( 0.50000000f,-0.50000000f,-0.50000000f,-0.50000000f),
+
+// 24 quats ( 0,0, 0.3826, 0.9238 )
+
+      new Static4D ( 0.00000000f, 0.00000000f, 0.38268343f, 0.92387950f),
+      new Static4D ( 0.00000000f, 0.00000000f, 0.38268343f,-0.92387950f),
+      new Static4D ( 0.00000000f, 0.00000000f, 0.92387950f, 0.38268343f),
+      new Static4D ( 0.00000000f, 0.00000000f, 0.92387950f,-0.38268343f),
       new Static4D ( 0.00000000f, 0.38268346f, 0.00000000f, 0.92387950f),
-      new Static4D ( 0.00000000f, 0.70710677f, 0.00000000f, 0.70710677f),
+      new Static4D ( 0.00000000f, 0.38268328f, 0.00000000f,-0.92387962f),
+      new Static4D ( 0.00000000f,-0.38268328f,-0.92387962f, 0.00000000f),
+      new Static4D ( 0.00000000f,-0.38268346f, 0.92387950f, 0.00000000f),
       new Static4D ( 0.00000000f, 0.92387950f, 0.00000000f, 0.38268343f),
       new Static4D ( 0.00000000f, 0.92387950f, 0.00000000f,-0.38268352f),
-      new Static4D ( 0.00000000f, 0.70710677f, 0.00000000f,-0.70710677f),
-      new Static4D ( 0.00000000f, 0.38268328f, 0.00000000f,-0.92387962f),
-      new Static4D (-0.27059805f, 0.65328145f, 0.27059805f, 0.65328145f),
-      new Static4D (-0.65328145f, 0.27059805f, 0.65328145f, 0.27059805f),
-      new Static4D (-0.65328145f,-0.27059811f, 0.65328145f,-0.27059811f),
-      new Static4D (-0.27059793f,-0.65328151f, 0.27059793f,-0.65328151f),
-      new Static4D ( 0.00000000f, 0.00000000f, 0.70710677f, 0.70710677f),
-      new Static4D ( 0.27059805f,-0.27059805f, 0.65328145f, 0.65328145f),
-      new Static4D ( 0.49999997f,-0.49999997f, 0.49999997f, 0.49999997f),
-      new Static4D ( 0.65328145f,-0.65328145f, 0.27059805f, 0.27059805f),
-      new Static4D ( 0.70710677f,-0.70710677f,-0.00000003f,-0.00000003f),
-      new Static4D ( 0.65328145f,-0.65328145f,-0.27059811f,-0.27059811f),
-      new Static4D ( 0.49999997f,-0.49999997f,-0.49999997f,-0.49999997f),
-      new Static4D ( 0.27059793f,-0.27059793f,-0.65328151f,-0.65328151f),
+      new Static4D ( 0.00000000f,-0.92387950f,-0.38268352f, 0.00000000f),
+      new Static4D ( 0.00000000f,-0.92387950f, 0.38268343f, 0.00000000f),
+      new Static4D ( 0.38268346f, 0.00000000f, 0.00000000f, 0.92387950f),
+      new Static4D ( 0.38268328f, 0.00000000f, 0.00000000f,-0.92387962f),
+      new Static4D ( 0.38268328f, 0.00000000f,-0.92387962f, 0.00000000f),
+      new Static4D ( 0.38268346f, 0.00000000f, 0.92387950f, 0.00000000f),
+      new Static4D ( 0.38268325f,-0.92387950f, 0.00000000f, 0.00000000f),
+      new Static4D ( 0.38268325f, 0.92387950f, 0.00000000f, 0.00000000f),
+      new Static4D ( 0.92387950f, 0.00000000f, 0.00000000f,-0.38268352f),
+      new Static4D ( 0.92387950f, 0.00000000f, 0.00000000f, 0.38268343f),
+      new Static4D ( 0.92387950f, 0.00000000f, 0.38268343f, 0.00000000f),
+      new Static4D ( 0.92387950f, 0.00000000f,-0.38268352f, 0.00000000f),
+      new Static4D ( 0.92387950f, 0.38268343f, 0.00000000f, 0.00000000f),
+      new Static4D ( 0.92387950f,-0.38268343f, 0.00000000f, 0.00000000f),
+
+// 48 quats ( 0.2705, 0.2705, 0.6532, 0.6532 )
+
       new Static4D ( 0.27059805f, 0.27059805f, 0.65328145f, 0.65328145f),
-      new Static4D ( 0.49999997f, 0.49999997f, 0.49999997f, 0.49999997f),
-      new Static4D ( 0.65328145f, 0.65328145f, 0.27059805f, 0.27059805f),
-      new Static4D ( 0.65328145f, 0.65328145f,-0.27059811f,-0.27059811f),
-      new Static4D ( 0.49999997f, 0.49999997f,-0.49999997f,-0.49999997f),
       new Static4D ( 0.27059793f, 0.27059793f,-0.65328151f,-0.65328151f),
+      new Static4D ( 0.27059805f, 0.27059805f,-0.65328145f, 0.65328145f),
+      new Static4D ( 0.27059793f, 0.27059793f, 0.65328151f,-0.65328151f),
+      new Static4D ( 0.27059805f,-0.27059805f, 0.65328145f,-0.65328145f),
+      new Static4D ( 0.27059793f,-0.27059793f,-0.65328151f, 0.65328151f),
+      new Static4D ( 0.27059805f,-0.27059805f, 0.65328145f, 0.65328145f),
+      new Static4D ( 0.27059793f,-0.27059793f,-0.65328151f,-0.65328151f),
+      new Static4D ( 0.27059808f, 0.65328145f, 0.27059802f,-0.65328145f),
+      new Static4D ( 0.27059799f, 0.65328145f, 0.27059799f, 0.65328145f),
+      new Static4D ( 0.27059802f, 0.65328145f,-0.27059802f,-0.65328145f),
+      new Static4D ( 0.27059793f, 0.65328151f,-0.27059793f, 0.65328151f),
       new Static4D ( 0.27059799f, 0.65328145f, 0.65328145f, 0.27059799f),
-      new Static4D (-0.27059799f, 0.65328145f, 0.65328145f,-0.27059799f),
-      new Static4D (-0.65328145f, 0.27059796f, 0.27059796f,-0.65328145f),
-      new Static4D (-0.65328145f,-0.27059814f,-0.27059814f,-0.65328145f),
-      new Static4D ( 0.00000000f, 0.00000000f, 1.00000000f,-0.00000004f),
-      new Static4D (-0.00000002f,-0.38268346f, 0.92387950f,-0.00000004f),
-      new Static4D (-0.00000003f,-0.70710677f, 0.70710677f,-0.00000003f),
-      new Static4D (-0.00000004f,-0.92387950f, 0.38268343f,-0.00000002f),
-      new Static4D (-0.00000004f,-1.00000000f,-0.00000004f, 0.00000000f),
-      new Static4D (-0.00000004f,-0.92387950f,-0.38268352f, 0.00000002f),
-      new Static4D (-0.00000003f,-0.70710677f,-0.70710677f, 0.00000003f),
-      new Static4D (-0.00000002f,-0.38268328f,-0.92387962f, 0.00000004f),
-      new Static4D ( 0.38268346f,-0.00000002f, 0.92387950f,-0.00000004f),
-      new Static4D ( 0.70710677f,-0.00000003f, 0.70710677f,-0.00000003f),
-      new Static4D ( 0.92387950f,-0.00000004f, 0.38268343f,-0.00000002f),
-      new Static4D ( 0.92387950f,-0.00000004f,-0.38268352f, 0.00000002f),
-      new Static4D ( 0.70710677f,-0.00000003f,-0.70710677f, 0.00000003f),
-      new Static4D ( 0.38268328f,-0.00000002f,-0.92387962f, 0.00000004f),
+      new Static4D ( 0.27059799f, 0.65328145f, 0.65328145f,-0.27059799f),
+      new Static4D ( 0.27059808f, 0.65328145f,-0.65328145f, 0.27059808f),
+      new Static4D ( 0.27059796f, 0.65328145f,-0.65328145f,-0.27059796f),
+      new Static4D ( 0.27059808f,-0.65328145f, 0.27059814f, 0.65328145f),
+      new Static4D ( 0.27059799f,-0.65328145f, 0.27059799f,-0.65328145f),
+      new Static4D ( 0.27059805f,-0.65328145f,-0.27059805f,-0.65328145f),
+      new Static4D ( 0.27059799f,-0.65328145f,-0.27059799f, 0.65328145f),
+      new Static4D ( 0.27059814f,-0.65328145f, 0.65328145f,-0.27059814f),
+      new Static4D ( 0.27059799f,-0.65328145f, 0.65328145f, 0.27059799f),
+      new Static4D ( 0.27059799f,-0.65328145f,-0.65328145f,-0.27059799f),
+      new Static4D ( 0.27059799f,-0.65328145f,-0.65328145f, 0.27059799f),
+      new Static4D ( 0.65328145f, 0.27059814f, 0.27059814f, 0.65328145f),
+      new Static4D ( 0.65328145f, 0.27059799f, 0.27059799f,-0.65328145f),
+      new Static4D ( 0.65328145f, 0.27059799f,-0.27059799f,-0.65328145f),
+      new Static4D ( 0.65328145f, 0.27059799f,-0.27059799f, 0.65328145f),
       new Static4D ( 0.65328145f, 0.27059802f, 0.65328145f,-0.27059808f),
-      new Static4D ( 0.27059808f, 0.65328145f, 0.27059802f,-0.65328145f),
-      new Static4D (-0.27059808f, 0.65328145f,-0.27059814f,-0.65328145f),
-      new Static4D (-0.65328151f, 0.27059796f,-0.65328151f,-0.27059790f),
-      new Static4D ( 0.00000000f, 0.00000000f, 0.70710677f,-0.70710677f),
-      new Static4D (-0.27059805f,-0.27059805f, 0.65328145f,-0.65328145f),
-      new Static4D (-0.49999997f,-0.49999997f, 0.49999997f,-0.49999997f),
-      new Static4D (-0.65328145f,-0.65328145f, 0.27059805f,-0.27059805f),
-      new Static4D (-0.70710677f,-0.70710677f,-0.00000003f, 0.00000003f),
-      new Static4D (-0.65328145f,-0.65328145f,-0.27059811f, 0.27059811f),
-      new Static4D (-0.49999997f,-0.49999997f,-0.49999997f, 0.49999997f),
-      new Static4D (-0.27059793f,-0.27059793f,-0.65328151f, 0.65328151f),
-      new Static4D ( 0.27059805f,-0.27059805f, 0.65328145f,-0.65328145f),
-      new Static4D ( 0.49999997f,-0.49999997f, 0.49999997f,-0.49999997f),
+      new Static4D ( 0.65328145f, 0.27059802f, 0.65328145f, 0.27059802f),
+      new Static4D ( 0.65328145f, 0.27059811f,-0.65328145f, 0.27059811f),
+      new Static4D ( 0.65328145f, 0.27059802f,-0.65328145f,-0.27059802f),
+      new Static4D ( 0.65328145f,-0.27059799f, 0.27059799f,-0.65328145f),
+      new Static4D ( 0.65328145f,-0.27059799f, 0.27059799f, 0.65328145f),
+      new Static4D ( 0.65328145f,-0.27059799f,-0.27059799f,-0.65328145f),
+      new Static4D ( 0.65328145f,-0.27059796f,-0.27059796f, 0.65328145f),
+      new Static4D ( 0.65328151f,-0.27059796f, 0.65328151f, 0.27059790f),
+      new Static4D ( 0.65328145f,-0.27059799f, 0.65328145f,-0.27059799f),
+      new Static4D ( 0.65328145f,-0.27059799f,-0.65328145f, 0.27059799f),
+      new Static4D ( 0.65328145f,-0.27059805f,-0.65328145f,-0.27059805f),
+      new Static4D ( 0.65328145f, 0.65328145f, 0.27059805f, 0.27059805f),
+      new Static4D ( 0.65328145f, 0.65328145f,-0.27059811f,-0.27059811f),
+      new Static4D ( 0.65328145f, 0.65328145f, 0.27059811f,-0.27059811f),
+      new Static4D ( 0.65328145f, 0.65328145f,-0.27059805f, 0.27059805f),
+      new Static4D ( 0.65328145f,-0.65328145f, 0.27059805f, 0.27059805f),
+      new Static4D ( 0.65328145f,-0.65328145f,-0.27059811f,-0.27059811f),
       new Static4D ( 0.65328145f,-0.65328145f, 0.27059805f,-0.27059805f),
       new Static4D ( 0.65328145f,-0.65328145f,-0.27059811f, 0.27059811f),
-      new Static4D ( 0.49999997f,-0.49999997f,-0.49999997f, 0.49999997f),
-      new Static4D ( 0.27059793f,-0.27059793f,-0.65328151f, 0.65328151f),
-      new Static4D ( 0.65328145f,-0.27059799f, 0.27059799f,-0.65328145f),
-      new Static4D ( 0.65328145f, 0.27059799f,-0.27059799f,-0.65328145f),
-      new Static4D ( 0.27059796f, 0.65328145f,-0.65328145f,-0.27059796f),
-      new Static4D (-0.27059814f, 0.65328145f,-0.65328145f, 0.27059814f),
+
+// 96 quats ( 0.8535, 0.3535, 0.3535, 0.1464 )
+
+      new Static4D ( 0.14644665f, 0.35355335f, 0.35355338f, 0.85355335f),
+      new Static4D ( 0.14644665f, 0.35355335f, 0.35355335f,-0.85355335f),
+      new Static4D ( 0.14644660f, 0.35355338f,-0.35355338f, 0.85355335f),
+      new Static4D ( 0.14644653f, 0.35355324f,-0.35355340f,-0.85355340f),
+      new Static4D ( 0.14644665f, 0.35355335f, 0.85355335f,-0.35355338f),
+      new Static4D ( 0.14644657f, 0.35355335f, 0.85355335f, 0.35355330f),
+      new Static4D ( 0.14644663f, 0.35355340f,-0.85355335f, 0.35355340f),
+      new Static4D ( 0.14644665f, 0.35355335f,-0.85355335f,-0.35355338f),
+      new Static4D ( 0.14644665f,-0.35355335f, 0.35355338f,-0.85355335f),
+      new Static4D ( 0.14644665f,-0.35355335f, 0.35355338f, 0.85355335f),
+      new Static4D ( 0.14644660f,-0.35355338f,-0.35355338f,-0.85355335f),
+      new Static4D ( 0.14644653f,-0.35355324f,-0.35355340f, 0.85355340f),
+      new Static4D ( 0.14644660f,-0.35355340f, 0.85355335f, 0.35355335f),
+      new Static4D ( 0.14644665f,-0.35355335f, 0.85355335f,-0.35355338f),
+      new Static4D ( 0.14644657f,-0.35355335f,-0.85355335f, 0.35355330f),
+      new Static4D ( 0.14644665f,-0.35355335f,-0.85355335f,-0.35355338f),
+      new Static4D ( 0.14644657f, 0.85355335f, 0.35355330f, 0.35355335f),
+      new Static4D ( 0.14644660f, 0.85355335f,-0.35355338f, 0.35355338f),
+      new Static4D ( 0.14644657f, 0.85355335f, 0.35355335f,-0.35355330f),
+      new Static4D ( 0.14644663f, 0.85355335f,-0.35355335f,-0.35355335f),
+      new Static4D ( 0.14644665f,-0.85355335f,-0.35355335f,-0.35355338f),
+      new Static4D ( 0.14644665f,-0.85355335f, 0.35355335f, 0.35355338f),
+      new Static4D ( 0.14644665f,-0.85355335f, 0.35355335f,-0.35355338f),
+      new Static4D ( 0.14644662f,-0.85355335f,-0.35355347f, 0.35355340f),
+      new Static4D ( 0.85355335f, 0.14644660f, 0.35355338f, 0.35355338f),
+      new Static4D ( 0.85355335f, 0.14644657f, 0.35355340f,-0.35355340f),
+      new Static4D ( 0.85355335f, 0.14644659f,-0.35355335f,-0.35355335f),
+      new Static4D ( 0.85355335f, 0.14644656f,-0.35355335f, 0.35355341f),
+      new Static4D ( 0.85355335f,-0.14644656f, 0.35355335f, 0.35355341f),
+      new Static4D ( 0.85355335f,-0.14644656f,-0.35355335f, 0.35355341f),
+      new Static4D ( 0.85355335f,-0.14644665f, 0.35355338f,-0.35355344f),
+      new Static4D ( 0.85355335f,-0.14644656f,-0.35355335f,-0.35355341f),
+      new Static4D ( 0.85355335f, 0.35355347f, 0.14644665f, 0.35355335f),
+      new Static4D ( 0.85355335f, 0.35355347f, 0.14644665f,-0.35355335f),
+      new Static4D ( 0.85355335f, 0.35355347f,-0.14644665f,-0.35355335f),
+      new Static4D ( 0.85355335f, 0.35355335f,-0.14644662f, 0.35355338f),
+      new Static4D ( 0.85355335f, 0.35355335f, 0.35355338f, 0.14644662f),
+      new Static4D ( 0.85355335f, 0.35355338f, 0.35355338f,-0.14644660f),
+      new Static4D ( 0.85355335f, 0.35355347f,-0.35355335f, 0.14644665f),
+      new Static4D ( 0.85355335f, 0.35355335f,-0.35355344f,-0.14644663f),
+      new Static4D ( 0.85355335f,-0.35355347f, 0.14644665f,-0.35355335f),
+      new Static4D ( 0.85355335f,-0.35355335f, 0.14644662f, 0.35355338f),
+      new Static4D ( 0.85355335f,-0.35355347f,-0.14644665f,-0.35355335f),
+      new Static4D ( 0.85355335f,-0.35355338f,-0.14644662f, 0.35355338f),
+      new Static4D ( 0.85355335f,-0.35355338f, 0.35355338f, 0.14644663f),
+      new Static4D ( 0.85355335f,-0.35355335f, 0.35355338f,-0.14644662f),
+      new Static4D ( 0.85355335f,-0.35355338f,-0.35355335f,-0.14644662f),
+      new Static4D ( 0.85355335f,-0.35355348f,-0.35355344f, 0.14644666f),
+      new Static4D ( 0.35355341f, 0.35355341f,-0.14644663f, 0.85355335f),
+      new Static4D ( 0.35355340f, 0.35355338f, 0.14644662f, 0.85355335f),
+      new Static4D ( 0.35355335f, 0.35355330f, 0.14644657f,-0.85355335f),
+      new Static4D ( 0.35355335f, 0.35355335f,-0.14644659f,-0.85355335f),
+      new Static4D ( 0.35355335f, 0.35355335f, 0.85355335f, 0.14644659f),
+      new Static4D ( 0.35355340f, 0.35355335f,-0.85355335f, 0.14644663f),
+      new Static4D ( 0.35355338f, 0.35355335f, 0.85355335f,-0.14644665f),
+      new Static4D ( 0.35355340f, 0.35355344f,-0.85355335f,-0.14644659f),
+      new Static4D ( 0.35355341f,-0.35355341f,-0.14644663f,-0.85355335f),
+      new Static4D ( 0.35355341f,-0.35355341f, 0.14644663f, 0.85355335f),
+      new Static4D ( 0.35355341f,-0.35355341f,-0.14644663f, 0.85355335f),
+      new Static4D ( 0.35355324f,-0.35355340f, 0.14644654f,-0.85355350f),
+      new Static4D ( 0.35355341f,-0.35355341f,-0.85355335f,-0.14644663f),
+      new Static4D ( 0.35355341f,-0.35355341f, 0.85355335f,-0.14644663f),
+      new Static4D ( 0.35355341f,-0.35355341f, 0.85355335f, 0.14644663f),
+      new Static4D ( 0.35355338f,-0.35355320f,-0.85355350f, 0.14644657f),
+      new Static4D ( 0.35355341f, 0.14644663f, 0.35355341f, 0.85355335f),
+      new Static4D ( 0.35355341f, 0.14644663f, 0.35355341f,-0.85355335f),
+      new Static4D ( 0.35355338f, 0.14644662f,-0.35355335f, 0.85355335f),
+      new Static4D ( 0.35355341f, 0.14644663f,-0.35355341f,-0.85355335f),
+      new Static4D ( 0.35355341f, 0.14644663f, 0.85355335f, 0.35355341f),
+      new Static4D ( 0.35355335f, 0.14644657f, 0.85355335f,-0.35355340f),
+      new Static4D ( 0.35355338f, 0.14644660f,-0.85355335f, 0.35355338f),
+      new Static4D ( 0.35355324f, 0.14644653f,-0.85355350f,-0.35355338f),
+      new Static4D ( 0.35355340f,-0.14644659f, 0.85355340f, 0.35355320f),
+      new Static4D ( 0.35355341f,-0.14644663f, 0.85355335f,-0.35355341f),
+      new Static4D ( 0.35355338f,-0.14644660f,-0.85355335f,-0.35355338f),
+      new Static4D ( 0.35355324f,-0.14644656f,-0.85355350f, 0.35355344f),
+      new Static4D ( 0.35355341f,-0.14644663f, 0.35355341f,-0.85355335f),
+      new Static4D ( 0.35355341f,-0.14644663f, 0.35355341f, 0.85355335f),
+      new Static4D ( 0.35355335f,-0.14644656f,-0.35355327f, 0.85355335f),
+      new Static4D ( 0.35355341f,-0.14644663f,-0.35355341f,-0.85355335f),
+      new Static4D ( 0.35355338f, 0.85355335f, 0.14644660f, 0.35355338f),
+      new Static4D ( 0.35355320f, 0.85355335f, 0.14644654f,-0.35355338f),
+      new Static4D ( 0.35355324f, 0.85355340f,-0.14644653f, 0.35355340f),
+      new Static4D ( 0.35355335f, 0.85355335f,-0.14644665f,-0.35355347f),
+      new Static4D ( 0.35355335f, 0.85355335f, 0.35355347f,-0.14644665f),
+      new Static4D ( 0.35355320f, 0.85355335f, 0.35355338f, 0.14644654f),
+      new Static4D ( 0.35355327f, 0.85355335f,-0.35355335f,-0.14644656f),
+      new Static4D ( 0.35355340f, 0.85355335f,-0.35355338f, 0.14644662f),
+      new Static4D ( 0.35355320f,-0.85355335f, 0.14644654f, 0.35355338f),
+      new Static4D ( 0.35355338f,-0.85355335f, 0.14644662f,-0.35355335f),
+      new Static4D ( 0.35355335f,-0.85355335f,-0.14644665f, 0.35355347f),
+      new Static4D ( 0.35355338f,-0.85355335f,-0.14644660f,-0.35355338f),
+      new Static4D ( 0.35355324f,-0.85355341f, 0.35355338f,-0.14644653f),
+      new Static4D ( 0.35355335f,-0.85355335f, 0.35355338f, 0.14644659f),
+      new Static4D ( 0.35355335f,-0.85355335f,-0.35355347f,-0.14644665f),
+      new Static4D ( 0.35355320f,-0.85355335f,-0.35355338f, 0.14644654f),
+
+// 48 quats (0 - 1/2 - 1/2 - SQ2/2)
+
+      new Static4D ( 0.00000000f, 0.50000000f, 0.70710677f,-0.50000006f),
+      new Static4D ( 0.00000000f, 0.50000000f, 0.70710677f, 0.50000000f),
+      new Static4D ( 0.00000000f, 0.50000000f,-0.70710677f,-0.50000006f),
+      new Static4D ( 0.00000000f, 0.50000000f,-0.70710677f, 0.50000000f),
+      new Static4D ( 0.00000000f, 0.50000000f,-0.50000000f, 0.70710677f),
+      new Static4D ( 0.00000000f, 0.50000000f,-0.50000000f,-0.70710670f),
+      new Static4D ( 0.00000000f, 0.50000000f, 0.50000006f, 0.70710677f),
+      new Static4D ( 0.00000000f, 0.50000000f, 0.50000006f,-0.70710677f),
+      new Static4D ( 0.00000000f, 0.70710677f,-0.50000000f, 0.50000000f),
+      new Static4D ( 0.00000000f, 0.70710677f, 0.50000000f,-0.50000000f),
+      new Static4D ( 0.00000000f, 0.70710677f, 0.50000000f, 0.50000000f),
+      new Static4D ( 0.00000000f, 0.70710677f,-0.50000000f,-0.50000000f),
+      new Static4D ( 0.50000000f, 0.00000000f,-0.50000000f,-0.70710670f),
+      new Static4D ( 0.50000000f, 0.00000000f,-0.50000000f, 0.70710670f),
+      new Static4D ( 0.50000000f, 0.00000000f, 0.50000000f,-0.70710670f),
+      new Static4D ( 0.50000000f, 0.00000000f, 0.50000000f, 0.70710677f),
+      new Static4D ( 0.50000000f, 0.00000000f, 0.70710677f, 0.50000000f),
+      new Static4D ( 0.50000000f, 0.00000000f,-0.70710677f, 0.50000000f),
+      new Static4D ( 0.50000000f, 0.00000000f,-0.70710677f,-0.50000000f),
+      new Static4D ( 0.50000000f, 0.00000000f, 0.70710677f,-0.50000000f),
+      new Static4D ( 0.50000000f,-0.50000000f, 0.00000000f, 0.70710670f),
+      new Static4D ( 0.50000000f, 0.50000000f, 0.00000000f, 0.70710670f),
+      new Static4D ( 0.50000000f, 0.50000000f, 0.00000000f,-0.70710670f),
+      new Static4D ( 0.50000000f,-0.50000000f, 0.00000000f,-0.70710670f),
+      new Static4D ( 0.50000000f, 0.50000000f, 0.70710677f, 0.00000000f),
+      new Static4D ( 0.50000000f,-0.50000000f,-0.70710677f, 0.00000000f),
+      new Static4D ( 0.50000000f, 0.50000000f,-0.70710677f, 0.00000000f),
+      new Static4D ( 0.50000000f,-0.50000000f, 0.70710677f, 0.00000000f),
+      new Static4D ( 0.50000000f, 0.70710670f, 0.00000000f,-0.50000000f),
+      new Static4D ( 0.50000000f, 0.70710677f, 0.00000000f, 0.50000000f),
+      new Static4D ( 0.50000000f,-0.70710670f, 0.00000000f,-0.50000000f),
+      new Static4D ( 0.50000000f,-0.70710677f, 0.00000000f, 0.50000000f),
+      new Static4D ( 0.50000000f, 0.70710677f,-0.50000000f, 0.00000000f),
+      new Static4D ( 0.50000000f, 0.70710677f, 0.50000000f, 0.00000000f),
+      new Static4D ( 0.50000000f,-0.70710677f,-0.50000000f, 0.00000000f),
+      new Static4D ( 0.50000000f,-0.70710677f, 0.50000000f, 0.00000000f),
+      new Static4D ( 0.70710677f, 0.00000000f, 0.50000000f,-0.50000000f),
+      new Static4D ( 0.70710670f, 0.00000000f,-0.50000000f,-0.50000000f),
+      new Static4D ( 0.70710670f, 0.00000000f,-0.50000000f, 0.50000000f),
+      new Static4D ( 0.70710670f, 0.00000000f, 0.50000000f, 0.50000000f),
+      new Static4D ( 0.70710670f, 0.50000000f, 0.00000000f,-0.50000000f),
+      new Static4D ( 0.70710670f, 0.50000000f, 0.00000000f, 0.50000000f),
+      new Static4D ( 0.70710670f,-0.50000000f, 0.00000000f, 0.50000000f),
+      new Static4D ( 0.70710670f,-0.50000000f, 0.00000000f,-0.50000000f),
+      new Static4D ( 0.70710670f,-0.50000000f, 0.50000000f, 0.00000000f),
+      new Static4D ( 0.70710670f, 0.50000000f,-0.50000000f, 0.00000000f),
+      new Static4D ( 0.70710670f, 0.50000000f, 0.50000000f, 0.00000000f),
+      new Static4D ( 0.70710670f,-0.50000000f,-0.50000000f, 0.00000000f),
       };
     }
 
@@ -290,9 +472,9 @@ public class TwistyMixup extends ShapeHexahedron
     {
     if( mQuatIndex==null )
       {
-      mQuatIndex = new int[] { 0,2,6,4,9,40,36,38,
-                               0,18,6,54,12,45,48,9,2,20,4,56,
-                               0,4,2,6,12,9 };
+      mQuatIndex = new int[] { 0,10,11,3,6,2,1,8,
+                               0,4,11,5,7,12,13,6,10,20,3,18,
+                               0,3,10,11,7,6 };
       }
 
     return mObjectQuats[mQuatIndex[cubit]];
