It does not have a special name but the shoes are called point
shoes
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eHow Tips on Shoes for Disney World - 2013 was released on:
USA: 15 November 2013
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saddle shoes, not wing tips
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There are two types of Irish dancing shoes: hard shoes and soft
shoes. Hard shoes are similar to tap shoes, but have fiberglass
tips and heels. The soft shoes are similar to American style jazz
shoes.
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Ballet shoes.
or pointe shoes which are the ones that allow ballerinas to rise
on the tips of their toes