Of the 6 remaining pentagons one has its centre on the arctic circle and another on the antarctic circle .

The centre of the pentagon at the arctic circle is at-

66°34N (90°-23°26) 156°E (Siberian mountains)

At this centre,when the declination of the sun is 23°26 (21 June, Cancer), the sun is at its highest position giving 24 hours of daylight.

The centre of the pentagon at the antarctic circle is at-

66°34S (90°-23°26) 24°W (7° south of the Sandwich islands)

At this centre, when the declination of the sun is -23°26 (21December, Capricorn), the sun rises for the first time after 24 hours night-time.

The centres of the four remaining pentagons are found at the crossing points of the meridians which join the already established pentagons.

The centre of one pentagon is at 40°18N 90°W (Illinois, USA)

At 20°9N (the half of 40°18) the sun enters the signs of Gemini and Leo as it passes over the zenith.

At 40°18N, when the declination of the sun is 20°9, the sunrise follows the path of one of the meridians crossing the centre of the pentagon (the azimut of the sun is + or – 117°).

The centre of the opposing pentagon is at 40°18S 90°E (centre of the Indian Ocean).

At 20°9S (the half of 40°18) the sun enters the signs of Aquarius and Sagittarius as it passes over the zenith.

At 40°18S, when the declination of the sun is -20°9, the sunrise follows the path of one of the meridians crossing the centre of the pentagon (the azimut of the sun is +or – 63°).

The centres of the ten pentagons located so far correspond with the passage of the sun into all twelve signs of the zodiac. The two remaining centres of pentagons are different in that they indicate the sun’s quarter days.

They are at 46°52N 2°24E (Plaimpied abbey, south of Bourges, France) and 46°52S 177°36W (Bounty Island). 46°52 is twice the latitude of the tropics of Cancer (23°26N) and Capricorn (23°26S).

At these two places, when the sun is at a declination of +or- 15°17, it rises parallel to the ecliptic ( 90° to the angle of the poles of the ecliptic ,23°26). It should also be noted that the moon follows practically the same path as the ecliptic.

Place Declination of sun Date of sunrise

46°52N (Bourges) 15°17 1 May and 11 August (quarter days)

46°52S (Bounty -15°17 4 November and 7 February (quarter days)

Island)

See drawings B and C

Drawing B