You can either dot down to the points using TargetPath, or convert the Polygon over to a Path containing a PathGeometry:
<Canvas xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
<Canvas.Triggers>
<EventTrigger RoutedEvent="Canvas.Loaded">
<BeginStoryboard>
<Storyboard>
<PointAnimation
By="-20,-20"
Duration="0:0:2"
RepeatBehavior="Forever"
AutoReverse="True"
Storyboard.TargetName="figure1"
Storyboard.TargetProperty="StartPoint"/>
<PointAnimation
By="40,40"
Duration="0:0:2"
RepeatBehavior="Forever"
AutoReverse="True"
Storyboard.TargetName="segment1"
Storyboard.TargetProperty="Point"/>
<PointAnimation
By="50,40"
Duration="0:0:2"
RepeatBehavior="Forever"
AutoReverse="True"
Storyboard.TargetName="segment2"
Storyboard.TargetProperty="Point"/>
<PointAnimation
By="-20,30"
Duration="0:0:2"
RepeatBehavior="Forever"
AutoReverse="True"
Storyboard.TargetName="segment3"
Storyboard.TargetProperty="Point"/>
</Storyboard>
</BeginStoryboard>
</EventTrigger>
</Canvas.Triggers>
<Path Name="path" Fill="#20000000">
<Path.Data>
<PathGeometry>
<PathGeometry.Figures>
<PathFigureCollection>
<PathFigure x:Name="figure1" IsFilled="True" StartPoint="10, 100">
<PathFigure.Segments>
<PathSegmentCollection>
<LineSegment x:Name="segment1" Point="20, 20" />
<LineSegment x:Name="segment2" Point="90, 100" />
<LineSegment x:Name="segment3" Point="90, 200" />
</PathSegmentCollection>
</PathFigure.Segments>
</PathFigure>
</PathFigureCollection>
</PathGeometry.Figures>
</PathGeometry>
</Path.Data>
</Path>
</Canvas>