The 5-cell, or pentatope, is the self-dual fourth-dimensional analogue of the tetrahedron, with Coxeter group symmetry 
  
    
      
        
          
            A
          
          
            4
          
        
      
    
    {\displaystyle \mathrm {A} _{4}}
   of order 120 = 5! and 
  
    
      
        
          
            S
          
          
            5
          
        
      
    
    {\displaystyle \mathrm {S} _{5}}
   group structure.
Presentation
IDF typically presents as a solitary painless, smooth, flesh-colored to red, dome-shaped nodule located on the dorsal or lateral aspect of a finger or toe but sparing the thumb or great toe; they occur principally in the first two years of life with about 1/3 of cases having a lesion since birth. However: 1) lesions with appearances similar to, and diagnosed as, IPF have been described in extra digital sites such as the arm, breast, tongue, thigh, and chest; 2) unusual cases have presented with multiple lesions, i.e. 2–3, uncommonly 7–15, and one case with 74 lesions in a 2018 review study; 3) cases have been reported in children up to the age 10 and one case was reported in a 52-year-old adult; 4) the lesions are typically smaller than 2 cm in maximum diameter but rarely have been tumor-sized, e.g. 4.5 cm; 5) the lesions, particularly when larger-sized, may be painful and/or compromise the functions of nearby joints and digits; and 6) the lesions occasionally invade the periosteum and erode a nearby bone. Pathology
Microscopic histopathological analyses of appropriately dye-stained IDF tissues typically show a non-encapsulated small tumor composed of bundles of uniform spindle-shaped cells that combine physical features of fibroblasts (the most common cell type in connective tissue) with those of myofibroblasts  (contractile, spindle-shaped cells that are identifiable by their expression of α-smooth muscle actin) in a background of collagen fibers. In hematoxylin and eosin-stained tissues, the spindle-shaped cells have pale eosinophilic (i.e.