What about boxes (or just paper shapes) as say your polygons, some string as your lines, balls (that you can open up) as your points and marbles that you can put inside your balls as your attributes for your points? You could then do some spatial statistics work based on this as you'd have all the elements. I like the idea of you maybe have two boxes that each have 3 balls inside. But when you take into account marbles/attributes you might see that the balls in box 1 have more marbles inside or more of a certain colour or size.That way you can tell the story that visualization is one thing but can be totally different once you consider the attributes of each of the elements.You can then bring in different statistics measures, or bring in string/lines to split the boxes/polygons. You could also use your props to talk about topological relationships. And you can always throw a paper map underneath it all to act as your base map.
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At present you can create a web application on ArcGIS Online using one of the templates provided. Some of these have the capability to tweak the look and feel of them. They also have the capability to download the template and tweak the code to further configure the web app but you then have to host this on your own web server (even though all of the data may be coming from ArcGIS Online). It would be great for those organisations that don't have their own webserver but want a more customized web app if they could host these alongside their data in their ArcGIS Online for Organisations Subscription account.
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