About the 'vajra', Chris Wilkinson

Generally speaking, the thing that we call a “vajra” is of four sorts: The Vajra of Reality, the Symbolic Vajra, the Secret Vajra of Method, and the Material Vajra. In this case we are working with symbols, so this is about the Symbolic Vajra. A nine pointed vajra is a Samaya Vajra. A five pointed vajra is a Wisdom Vajra. A three pointed one is a Vajra to Drive Away the Inappropriate. The spread-horned one is a Vajra of Wrath. Whichever you may use, there are horns to both left and right, and there is the mid-section. The mid-section is round and at its ends there are a certain number of horns that stick out straight. The Saṃpuṭa says:

Pick it up at the place that holds three points.
The belt part is the best.

The size is generally between eight and twenty eight fingerwidths. On a nine pointed one, the nine horns on the upper part in the four directions are Akshobhya, Ratnasambhava, Amitabha, and Amoghasiddhi. The intermediate ones are their four consorts. The one at the center is the sky, Samanthabhadra. The tips are Vairocana’s pure essence. The nine horns on the lower part are the pure essence of the five wisdoms and the four immeasurables. Their tips are the pure essence of the Dharmadhatu, Great Bliss. The fact that these horns come out from the mouth of a Makara is a symbol for pulling us out from the pain at life’s roots. The moon throne for these horns is a symbol for cooling down the torments by which we measure samsara. The eight lotus petals on top are symbolic of the eight dear Bodhisattva children. Those below are the pure essence of the eight goddesses: Hook, Noose, Chains, Bell, Scold, Jewel Lightning, Leg Iron, and She that None Other Can Handle. The round center is a symbol to signify that the dominion of the Dharma is not complicated. The strings of pearls that ornament the two sides of the center symbolize that everything in samsara and nirvana is an adornment, and appears to us as a play.

Regarding the five-pointed Wisdom Vajra, the five horns at the top are the five wisdoms of the five lineages. The five horns at the bottom symbolize the total purity of the five consorts. The rest of it is the same as in the above.

Chris Wilkinson
An Overview of Tantra and Related Works (Sakya Kongma Series ) (Volume 4)