Is it possible to “Add a page” in Tumblr use “Custom Layout” and insert this code
{block:Posts}
{block:Text}
<li><img src="http://static.tumblr.com/taio0pf/aX1l4qwei/article-icon.png" />{Permalink}</li>
{/block:Text}
{block:Photo}
<li><img src="http://static.tumblr.com/taio0pf/WuHl4qwg3/photo-icon.png" />{Permalink}</li>
{/block:Photo}
{block:Link}
<li><img src="http://static.tumblr.com/taio0pf/TpTl4qwge/link-icon.png" />{Permalink}</li>
{/block:Link}
{/block:Posts}
This special Tumblr markup can’t work on custom pages, because no blog posts are associated. It only works for the theme (Customize appearance → Edit HTML).
You’d have to use a Custom Layout for your pages and use HTML directly.
I assume you want to list all your blog posts sorted by type (text, photo, link). You’d have to link each post manually. Or instead you could tag your posts by type and link the tags on this custom page.