Acronym sistic
Name small stellated icositetrachoron,
compound of 6 hex,
compound of 2 stico
Circumradius 1/sqrt(2) = 0.707107
Inradius 1/sqrt(8) = 0.353553
Coordinates
  • (1/sqrt(2), 0, 0, 0)                                             & all permutations, all changes of sign
    (vertex inscribed first hex component)
  • (±1/sqrt(8), ±1/sqrt(8), ±1/sqrt(8), ±1/sqrt(8))   & all permutations, even number of minus signs
    (vertex inscribed second hex component)
  • (±1/sqrt(8), ±1/sqrt(8), ±1/sqrt(8), ±1/sqrt(8))   & all permutations, odd number of minus signs
    (vertex inscribed third hex component)
  • (1/2, 1/2, 0, 0)                                                  & all permutations, all changes of sign
    (vertex inscribed dual stico component)
General of army stoc
Dual gistic
Confer
compound-component:
hex   stico  
general polytopal classes:
regular  
External
links 		polytopewiki  

Comes in 4 types, depending on the pairs of co-realmic tet (in dual positioning): being counted separately (type A,C) or being combined to so compounds as well (type B,D), and whether the components are being considered to be hexes (type A,B), or to be sticoes (type C,D).

As the snub of tes is nothing but hex, accordingly the snub of gico will be stico.


Incidence matrix according to Dynkin symbol

(Type A)

  48 ♦   6 |  12 |  8 || 1
-----+-----+-----+----++--
   2 | 144 |   4 |  4 || 1
-----+-----+-----+----++--
   3 |   3 | 192 |  2 || 1
-----+-----+-----+----++--
♦  4 |   6 |   4 | 96 || 1
-----+-----+-----+----++--
♦  8 |  24 |  32 | 16 || 6


(Type B)

  48 ♦   6 |  12 |  8 || 1
-----+-----+-----+----++--
   2 | 144 |   4 |  4 || 1
-----+-----+-----+----++--
   3 |   3 | 192 |  2 || 1
-----+-----+-----+----++--
♦  8 |  12 |   8 | 48 || 2
-----+-----+-----+----++--
♦  8 |  24 |  32 | 16 || 6


(Type C)

  48 ♦   6 |  12 |  8 || 1
-----+-----+-----+----++--
   2 | 144 |   4 |  4 || 1
-----+-----+-----+----++--
   3 |   3 | 192 |  2 || 1
-----+-----+-----+----++--
♦  4 |   6 |   4 | 96 || 1
-----+-----+-----+----++--
♦ 24 |  72 |  96 | 48 || 2


(Type D)

  48 ♦   6 |  12 |  8 || 1
-----+-----+-----+----++--
   2 | 144 |   4 |  4 || 1
-----+-----+-----+----++--
   3 |   3 | 192 |  2 || 1
-----+-----+-----+----++--
♦  8 |  12 |   8 | 48 || 2
-----+-----+-----+----++--
♦ 24 |  72 |  96 | 48 || 2

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