Twisted Honeycombs

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American Mathematical Soc., 1970 - Mathematics - 47 pages
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Contents

Introduction
1
Regular tessellations
2
Finite groups of rotations
3
Groups generated by two or three reflections
5
The Pelrie polygon of a tessellation
8
The regular tessellations ip q
11
Threedimensional honeycombs
14
The simplex cube cross polytope and 24cell
17
The 120cell and the 600cell Imagine a pillar formed by ten solid dodecahedra D D
19
Groups generated by four reflections
24
The Petrie polygon of a honeycomb
25
The regular honeycombs p q r
28
Finite groups of quaternions The onecelled honeycombs
36
Quaternions and Petrie polygons
42
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