Introduction:
Nematocysts are specialized stinging cell organelles found in organisms belonging to the phylum Coelenterata. These organisms include jellyfish, sea anemones, and corals. Nematocysts are used for capturing prey, defense, and locomotion.

Explanation:
Nematocysts are unique to organisms belonging to the phylum Coelenterata. Let's understand why nematocysts are not found in the other given phyla:

Phylum - Porifera:
- Organisms belonging to the phylum Porifera are commonly known as sponges.
- Sponges do not possess specialized stinging cells or nematocysts.
- Instead, they have specialized cells called choanocytes that create water currents for filter feeding.

Phylum - Echinodermata:
- Organisms belonging to the phylum Echinodermata include starfish, sea urchins, and sea cucumbers.
- Echinoderms do not possess nematocysts.
- Instead, they have specialized structures called tube feet that aid in locomotion and feeding.

Phylum - Arthropoda:
- Organisms belonging to the phylum Arthropoda include insects, spiders, crustaceans, and centipedes.
- Arthropods do not possess nematocysts.
- They have various types of defensive mechanisms, such as poison glands, spines, and stingers, but nematocysts are not present.

Phylum - Coelenterata:
- Organisms belonging to the phylum Coelenterata, also known as Cnidaria, include jellyfish, sea anemones, and corals.
- These organisms possess specialized stinging cells called nematocysts.
- Nematocysts are capsule-like structures that contain a coiled thread-like tube with a barbed or venomous tip.
- When triggered, the nematocyst shoots out the thread, injecting venom into the prey or predator.

Conclusion:
Based on the information provided, nematocysts are found only in organisms belonging to the phylum Coelenterata. These specialized stinging cell organelles are not present in the phyla Porifera, Echinodermata, or Arthropoda.