The ring torus is one way to embed this space into Euclidean space, but another way to do this is the Cartesian product of the embedding of S1 in the plane with itself. This produces a geometric object called the Clifford torus, a surface in 4-space. In the field of topology, a torus is any topological space that is homeomorphic to a torus. The surface of a coffee cup and a doughnut are both topological tori with genus one. An example of a torus can be constructed by taking a rectangular strip of flexible material, for example, a rubber sheet, and joining the top edge to the bottom edge, and the left edge to the right edge, without any half-twists (compare Möbius strip). Geometry
A torus can be defined parametrically by:
where

θ, φ are angles which make a full circle, so their values start and end at the same point,
R is the distance from the center of the tube to the center of the torus,
r is the radius of the tube.Angle θ represents rotation around the tube, whereas φ represents rotation around the torus axis of revolution. R is known as the "major radius" and r is known as the "minor radius". The ratio R divided by r is known as the "aspect ratio". The typical doughnut confectionery has an aspect ratio of about 3 to 2.
duodenalis has been sub-classified into eight genetic assemblages (designated A–H). Genotyping of G. duodenalis isolated from various hosts has shown that assemblages A and B infect the largest range of host species, and appear to be the main and possibly only G. duodenalis assemblages that infect humans. Risk factors
According to the United States Centers for Disease Control and Prevention (CDC), people at greatest risk of infection are:

People in childcare settings
People who are in close contact with someone who has the disease
Travelers within areas that have poor sanitation
People who have contact with feces during sexual activity
Backpackers or campers who drink untreated water from springs, lakes, or rivers
Swimmers who swallow water from swimming pools, hot tubs, interactive fountains, or untreated recreational water from springs, lakes, or rivers
People who get their household water from a shallow well
People with weakened immune systems
People who have contact with infected animals or animal environments contaminated with fecesFactors that increase infection risk for people from developed countries include changing diapers, consuming raw food, owning a dog, and travelling in the developing world. However, 75% of infections in the United Kingdom are acquired in the UK, not through travel elsewhere. In the United States, giardiasis occurs more often in summer, which is believed to be due to a greater amount of time spent on outdoor activities and traveling in the wilderness. Transmission
Giardiasis is transmitted via the fecal-oral route with the ingestion of cysts. Primary routes are personal contact and contaminated water and food.