Roachmania

The word “cockroach” comes from the Spanish word “cucaracha.”
There are over 4,500 species of cockroaches worldwide (about 45 in North America alone) but only 30 of them are associated with man and only four are considered pests.
Cockroaches can live nine days without a head! They do not breathe through their mouth parts, rather through spiracles on their abdomen. They eventually die from lack of water.
Abundant variety of roach-like insects have been found as far back as 325 million years ago (the late Carboniferous period) sometimes described as “The Age of Cockroaches”. Modern roaches evolved around the Cretaceous period, yup... along side T-Rex.
The first insects that could fold their wings were cockroach-like species.
Cockroaches are most common in moist, forested environments, and especially prevalent in the Tropics and Subtropics. They are able to withstand extremely low temperatures (as low as -118 degrees Fahrenheit) with some species found in the Arctics while others are found in desert habitats.
Most Cockroaches feed on decaying plant matter (dead leaves, fungi, etc.) making it extremely beneficial to the health of their ecosystems.
Factsheet - Cockroach

Mantises are predatory modified cockroaches.
The word “mantis” comes from a Greek word meaning “prophet.”
There are over 2,300 species of mantises worldwide (about 20 in North America alone).
Their head can swivel 180° so the mantis can look around without moving its body.
Some species of mantises are the only animals in the world to have only one ear.

Termites and Cockroaches are more closely related and are now in the same insect order, Blattodea. 10% of the world’s biomass is composed of termites.
Factsheet - Termites