What are cardinal vowels in relation to English vowels?

Cardinal vowels are a linguistic construction devised by
Daniel Jones to organize a consistent vowel sound classification. The classification of
vowel sounds in the cardinal organization is based on two possible tongue positions.
These are the front-to-back and high-to-low positions.
Front-to-back signifies the positions of the tongue that
range from farthest forward at the teeth to farthest backward at the throat in vowel
formations. High-to-low signifies the positions of the
tongue that range from closest to the palette of the mouth to the furthest from the
palette in vowel formations.

These two possible positions,
front-to-back and high-to-low, always actualize in pairs on
any vowel. So the cardinal vowels are recorded on the cardinal quadrilateral chart (the
quadrilateral is a visualization of the perceived increasing size and shape of the mouth
while pronouncing vowel sounds) between the two extreme sounds represented by the pairs
high front and low back
(highest and forward most tongue position to lowest and furthest back tongue position).

The vowels of all languages can be located within the
variations of this cardinal quadrilateral for purposes of
language transcription. Since the cardinal system is imperfect and rigid, very narrow,
precise transcriptions are needed to record the deviations from the Primary and
Secondary cardinal vowels in various languages.

In
English, the cardinal vowels are linked to
lexical sets to standardize the perceptions of vowel
location along the high front to low back position pairs. All English varieties employ
the same phonemes, but not all varieties employ the phonemes in the same words. For
example, in British English (BE), Received Pronunciation, the word happy has an /i/
phoneme pronounced at the orthographic /y/, whereas American English (AE), General
American, has an /I/ phoneme pronounced at the orthographic /y/.  Another example, one
using a consonant diphthong, is that in Indian English, the BE fricative /th/ phoneme is
realized as a dental plosive.

Since all English varieties
use the same phonemes, each Primary and Secondary vowel is
assigned a lexical key word to standardized its position on the high front to low back
quadrilateral chart. Of the eight Primary cardinal vowels, the high front vowel is /i/
as in BE pronunciation of the lexical pair word Happy. It is front high tense. The next
is /e/ as in the diphthong in Face. It is front mid tense. Then comes the front mid lax
sound as in the /e/ in Letter. The last of the four high front vowel classifications is
the front low vowel as in the AE pronunciation of
Palm.

Switching to the four low back classifications, the
lowest one, the low back vowel, sounds like the AE pronunciation of Lot. The next
highest position is back low open-o as in the AE pronunciation of the lexical pair word
Cloth. It is back mid lax. Next is the low back /o/ sound in AE Goat. It is back mid
tense. The highest of the low back pairs is /u/ as in the AE lexical pair word Goose. It
is back high tense.