Ekimp you are correct about the frosted and gloss finish. The vases are made in five sections with some parts frosted and some gloss.
There are very few pedestal vases online and the ones that are seem to be mostly Harrach exhibition vases. The white vases are described as either alabaster , opaque, opal, frosted and opaline which one is correct I am not sure myself.
I will try to send some pictures to the Harrach museum.