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Subject: Halpern's Tetrahedron
From: mark.longridge@canrem.com (Mark Longridge)
Message-Id: <60.1258.5834.0C1FCC4E@canrem.com>
Date: Sun,  5 Nov 95 01:59:00 -0500
Organization: CRS Online  (Toronto, Ontario)

# Ben Halpern's Tetrahedron
# 4 faces rotate

tetra := Group(
  (1,3,5)(2,4,6)(7,13,24)(12,18,23)(11,17,22),
  (7,9,11)(8,10,12)(22,15,3)(2,21,14)(1,20,13),
  (13,15,17)(14,16,18)(11,20,5)(10,19,4)(9,24,3),
  (22,20,24)(21,19,23)(7,15,5)(8,16,6)(9,17,1)
);;

# Size (tetra) = 3,732,480;
#
# Centre (tetra) = (2,12)(4,18)(6,23)(8,21)(10,14)(16,19);
#
# Tetrahedron has 6 edges, 4 corners
#  6! /2 * 2^5 * 4!/2 * 3^3

Just a few more combinations than a 2x2x2 pocket cube...
 -> Mark <-