Here is a conical bore Boehm system piccolo
http://www.jupitermusic.com/jbi_instrumentDetails.aspx?cId=17&lId=2&sId=1&pId=539
Here are some more: http://www.johnpacker.co.uk/Catalogue/Woodwind/Flute-Piccolo/Piccolo
There are exceptions but it’s the norm for piccolos.
I’ve just noticed the thread title!
it’s good when a aural joke and cross into the visual
isn’t it 