Tai Chi Weapons Proper Names?

What's the proper name or names for the swords Tai Chi uses? What's the proper name of the fan that's used as well?

Weapons training and fencing applications employing the straight sword known as the jian or chien or gim (ji脿n), a heavier curved sabre, sometimes called a broadsword or tao (d膩o, which is actually considered a big knife), folding fan also called san, wooden staff (2 m) known as kun , 7 foot (2 m) spear and 13 foot (4 m) lance (both called qi膩ng). More exotic weapons still used by some traditional styles are the large Dadao or Ta Tao and Pudao or P'u Tao sabres, halberd (j菒 ), cane, rope-dart, three sectional staff, Wind and fire wheels, lasso, whip, chain whip and steel whip.

My Tai Chi weapon of choice is the cane / walking stick.
I have never heard it called anything except for a cane or a walking stick.
The Mandarin word for "cane" is "zh脿ng."

My studies have included regular canes (from functional "J" canes to the elegant and exotic) and rattan "L" canes which are a bit longer.

Single Sword (Dan Jian)
Single Broadsword (Dan Dao)
Pear Blossom Spear - White Ape Staff (Li Hua Qiang - Bai Yuan Gun)
Spring and Autumn Big Broadsword (Chun Qiu Dadao/Guandao)
Double Sword (Shuang Jian)
Double Broadsword (Shuang Dao)
Double Hooks (Shuang Gou)
Double Mace (Shuang Jian)
13 Long pole (Shi San Gan)
Two sectioned pole (Saozi Gan)