= Two-triangle disc and Möbius-band model of the projective plane
{c}
In a triangle whose two sides at an apex are glued with that apex fixed, cross-sections become circles and the apex becomes their <cone> point. This <quotient> is a <disc>. A second triangle with boundary word $aa b^{-1}$ becomes a <Möbius band> after the $a$ sides are identified. Gluing the remaining $b$ boundary to the first <disc> caps the band and gives the <real projective plane>. The resulting two-face cell structure has two vertices, three edges and <Euler characteristic> one.
Back to article page
