English ivy (Hedera helix) comes in many, many shapes and sizes, so in this case, trust the botanical name. I've never even heard of 'Polynesian' ivy. Should be just fine with your frogs.

Hedera helix is fairly poisonous, it often kills pet rabbits.

Why does everyone still think that frogs will eat their plants? And that anything poisonous to one animal is poisonouse to all other animals? It always depends on the amount ingested, and on what kind of animal it is. Cats will throw up if they eat ivy, therefore it is called 'poisonous' and the ASPCA puts it on their list of plants you should never have anywhere near your pets. My cat has never even tried to nibble my ivy, though he will eat some other plants. Frogs just don't eat stuff that doesn't move, and frogs aren't even mammals, so how can you assume that english ivy is poisonous to them? Sure, 'better safe than sorry', but the list of terrarium plants is restricted to about 5 that are 'safe' if you go by what various people say is poisonous. I'm not saying you're stupid or anything like that if you worry about poisonous plants, but I, personally, am not willing to have only broms, ferns, moss, and orchids in my terrs.