分析：

      将八面体置于3D坐标系中，其中心的坐标位于原点（0，0，0），让八面体的六个顶点恰好位于3D坐标系的x轴、y轴和z轴上，则从八面体的中心到这六个顶点的距离是相等的。我们可以假设这个距离为r，则六个顶点的坐标分别为上（0，-r，0）、下（0，r，0）、四周：左（-r，0，0）、右（r，0，0）、前（0，0，-r）、后（0，0，r）。

1 package 2 { 3     import flash.display.MovieClip; 4     import flash.display.Sprite; 5     import flash.events.Event; 6     import flash.geom.Point; 7     import flash.geom.Vector3D; 8      9     /**10      * @author Frost.Yen11      * @E-mail 871979853@qq.com12      * @create 2015-9-7 下午5:10:0513      *14      */15     [SWF(width="800",height="600")]16     public class LineOctahedron extends Sprite17     {18         private var _faceArr:Array = [];19         private var _r:Number = 100;//中心到顶点的距离20         private var _focus:Number = 200;//焦距21         private var _lineContainer:Sprite;22         private var _container:Sprite;23         private var _vertexArr:Array = [{x:0,y:_r,z:0},{x:-_r,y:0,z:0},{x:0,y:0,z:_r},{x:_r,y:0,z:0},{x:0,y:0,z:-_r},{x:0,y:-_r,z:0}];24         public function LineOctahedron()25         {26             initViews();27             initEventListeners();28         }29         private function initViews():void30         {31             _container = new Sprite();32             _lineContainer = new Sprite();33             _container.x = _lineContainer.x = 400;34             _container.y = _lineContainer.y = 300;35             this.addChild(_container);36             this.addChild(_lineContainer);37             createFace();38             39         }40         private function initEventListeners():void41         {42             this.addEventListener(Event.ENTER_FRAME,onEnterFrame);43         }44         private function onEnterFrame(e:Event):void45         {46             for (var i:int=0; i<_faceArr.length; i++)47             {48                 _faceArr[i].transform.matrix3D.appendRotation((mouseX-_lineContainer.x)/50,Vector3D.Y_AXIS);49                 _faceArr[i].transform.matrix3D.appendRotation((mouseY-_lineContainer.y)/50,Vector3D.X_AXIS);50                 _faceArr[i].Z = (_faceArr[i] as MovieClip).transform.getRelativeMatrix3D(_container).position.z;51                 _faceArr[i].X = (_faceArr[i] as MovieClip).transform.getRelativeMatrix3D(_container).position.x*(_focus/(_focus+_faceArr[i].Z));52                 _faceArr[i].Y = (_faceArr[i] as MovieClip).transform.getRelativeMatrix3D(_container).position.y*(_focus/(_focus+_faceArr[i].Z));53                 //利用焦距实现透视54             }55             _lineContainer.graphics.clear();56             _lineContainer.graphics.lineStyle(3,0x00ffff);57             for(i = 1;i<=4;i++){58                 //从上面连到四周;59                 _lineContainer.graphics.moveTo(_faceArr[0].X,_faceArr[0].Y);60                 _lineContainer.graphics.lineTo(_faceArr[i].X,_faceArr[i].Y);61                 //从下面连到四周;62                 _lineContainer.graphics.moveTo(_faceArr[5].X,_faceArr[5].Y);63                 _lineContainer.graphics.lineTo(_faceArr[i].X,_faceArr[i].Y);64                 //四周顶点互连;65                 _lineContainer.graphics.moveTo(_faceArr[i].X,_faceArr[i].Y);66                 _lineContainer.graphics.lineTo(_faceArr[i!=4?i+1:1].X,_faceArr[i!=4?i+1:1].Y);67             }68         }69         private function createFace():void70         {71             for(var i:int = 0;i<6;i++){72                 var mc:MovieClip = new MovieClip();73                 _container.addChild(mc);74                 _faceArr.push(mc);75                 mc.x = _vertexArr[i].x;76                 mc.y = _vertexArr[i].y;77                 mc.z = _vertexArr[i].z;78             }79         }80     }81 }